Despite the persistent shilling of Guillermo Vilas' coach-manager Svengali, the massive hirsute and forceful Rumanian Davis Cup player Ion Tirriac, no reasonable case can be made for Vilas as the No. 1 tennis player in the world.

The Argentine lefthander must first dislodge the arguable incumbents, Jimmy Connors and Bjorn Borg. He knows that and is looking forward to trying in the U.S. Open, beginning the last day of this month at Forest Hills, N.Y.

Nevertheless, Vilas' current winning streak of five consecutive tournaments and 28 matches is the single most remarkable achievement in pro tennis this year. Second choice: Vilas' 35 consecutive triumphs on clay courts, incorporating his current streak and the French Open, the first Grand Slam tournament victory of his career.

Vilas, who celebrated his 25th birthday yesterday, is sitting out this week's Canadian Open after his extraordinary back-to-back-to-back-to-back-to-back victories at Kitsbuechel, Austria; Washington; Louisville; South Orange; N.J., and Columbus, Ohio.

He is the first player to win five consecutive Grand Prix tournaments since the series was inaugurated in 1970, and his streak is the longest in men's pro tennis since Rod Laver won 31 straight matches in 1969, the year of his second Grand Slam. (Connors' season record in 1974 When he swept the Australian Open, Wimbledon and Forest Hills, was 95-4, but he never won 28 matches consecutively.)

"I think it's a superhuman effort." fellow pro Harold Solomon said yesterday of Vilas' string. "Especially during the summer, on clay, with the kind of heat and humidity we've had every week.

"The thing that makes it amazing it that he's won week in a nd week out with no rest. I have trouble playing three weeks. Connors seldom plays more than a couple in row. Borg is probably the strongest player any given week, but over the long haul I'd have to go with Vilas.

"Physically, the guy is like a bull. But you have to be just as strong mentally to keep winning every day, to maintain that concentration, and that's what has suprised me," Solomon went on. "I didn't think Vilas was that mentally tough, but I guess he's worked on it a lot."

Critics point out that slow, high-bouncing seaside Argentinian resort of mar del Plata.It perfectly suits his game, bassed on quickness, strength, perseverence, and heavily topspun ground strokes that he slugs from the backcourt, varying depth and place, in rallies that wilt players with less stamina and frustrate those with less patience.

But clay is laso the most physically taxing surface for tennis. Points are long, and even one-sided matches can consume great amounts of time and energy. That is why Vilas' current streak is so astounding. It has transcended day and night finals and the consequent quick getaways and rapid adjustment to new surroundings and conditions.

With Tiriac helping shield him from intrusions, organizing and structuring his practice sessions and off-court routine, Vilas paces himself well. As he has noted, he only hits his hard, flat serve when he most needs it, to get out of trouble or to put a wobbling opponent away.

Most of the time he spins in his first serve at three-quarters pace because the serve is not a dominant weapon on clay, and he prefers to conserve energy. "I do not think you can do both, serve hard and hit the ground strokes hard all the time," Vilas says, sensibly. he saves himself for those splendid sprints that can be so demoralizing to a foe, when he runs down an apparent winner and whacks an offensive shot from a seemingly defensive position.

Vilas can hit outright winners, particularly off the topsin backhand that is generally considered the best since Laver's, and will jump on and punish short balls. He can volley reasonably well, but more often chooses to wear down the baseliners and counter-punch the attackers, buzzing passing shots when they come to the net against him. His favorite shot is cross-court, off both sides, but he can go down the line with equal facility. He also has a deadly topspin lob, beautifully disguised becaused he hits it off both sides with the same motion as his passing shot, but with a last-second flick of the wrist.

Despite his great clay court teacnique and instincts, and the resultant astonishing consistency of his play the last five weeks, Vilas has no legitimate claim to the No. 1 ranking until he beats WCT champion Connors and Wimbledon champ Borg, who have been his nemeses on the pro tour. (Borg has won their five meetings two this year, and Connors is 2-0 lifetime against Vilas, having annihilated him in their only meeting during the last five years, in the semifinals of last year's U.S. Open.)

Neither Connors nor Borg played in any of the tournaments in Vilas' current streak, or in the French. Neither did Manuel Orantes, who has come back from arm surgery and demonstrated the last two weeks that he is again a threat for the Forest Hills title he won over Connors in 1975.

For his six most recent tournament victories, Vilas has beaten Brian Gottfried in three finals (all straight sets), and Jan Kodes, Eddie Dibbs and Roscoe Tanner in the others. TOugh competition, to be sure, but to become King of the Hill, one traditionally must knock off the other pretenders to the throne, head to head.

Vilas acknowledges this even if Tiriac, the gloomy master of manipulation and psychological ploys, does not. After drubbing Gottfried, the No. 2 man in the Grand Prix standings, for the fourth consecutive tine Tuesday night in Columbus, Vilas was interviewed on the Public Broadcasting Service telecast and said: "I think I'm playing very well at this time, but I can't say I'm the No. 1 player in the world until I beat Connors and Borg. I have to beat them and maybe now they have to beat me."

At least Vilas has to win Forest Hills to stake his claim. If he does so without running into Connors or Borg, that is not his fault. If he beats one or both, he would have to beats one or both, he would have to be a contender for No.1 even though, exhausted by his effort to win the French, he lost listlessly to Billy Martin in the third round at Wimbledon.

Vilas was runner-up to Tanner in the Australian Open, on grass. (Those who argue that he can only play on clay should note that Vilas was also runner-up to Gottfried in the tough American Airlines Tennis Games on California hard courts, and before the French had taken his biggest career title, the Grand Prix Masters of 1974, on grass.) he has won nine of the 19 tournaments he has played this year, was runner-up in four more, and has compiled an 83-9 won-loss record, including Davis Cup.

"If I win Forest Hills, I will have two of the four big ones this year, and a final in another, so I should be No. 1," says Vilas, who will play only a $25,000 round-robin event at Rye, N.Y. (Aug. 25-29) before the U.S. "So for sure, I'm trying very hard."