Bernie Kosar, the University of Miami's redshirt sophomore quarterback who threw for nearly 6,000 yards in his 25-game collegiate career, turned professional today and immediately touched off what could become a high-stakes bidding war among as many as eight teams in the National Football League.

The Cleveland Browns and Minnesota Vikings have offered to trade combinations of starting players and/or draft picks to the Houston Oilers in exchange for the No. 2 pick in the April 30 NFL draft, and the right to pick Kosar.

(Buffalo, which will pick first, already has signed Virginia Tech defensive lineman Bruce Smith.)

The Browns, who have proposed two different trades that likely involve sending defensive starters to the Oilers, are the front-runners. Kosar, 21, who grew up in Youngstown, east of Cleveland, said during a news conference in Ohio today that he "would like nothing better than to play in Cleveland."

But others in the NFL are questioning his decision. At least three team executives, including General Manager Bobby Beathard of the Washington Redskins and Dick Steinberg, director of player development for the New England Patriots, said they would have advised him to stay in school another year.

"I'm disappointed he came out," Beathard said. "Personally, I wish he had stayed in school. The experience couldn't hurt him. Another year in college could do nothing but help him."

Another general manager, who asked not to be identified, questioned the judgment of turning pro at this time, when Kosar cannot be certain which team will draft him.

Al Davis of the Los Angeles Raiders admitted interest in the 6-foot-5, 210-pound dropback quarterback, but said he doesn't know enough about Kosar to decide if he should make an offer to the Oilers for the No. 2 pick.

"I like someone who gets the ball up the field, but I don't know if he's been attacked in the pocket yet," Davis said.

Kosar, who will need to take six credit hours this summer to graduate in three years from Miami, could not be timed or tested by pro scouts under NCAA rules.

He plans to complete his classes by the end of June, which would give him time for the NFL's summer training camps. Under league rules, underclassmen cannot enter the draft unless they have graduated ahead of time.

He became an instant star during his redshirt freshman year of 1983, when he led the Hurricanes to an 11-1 season and the mythical national championship.

It is unlikely things would happen so quickly if he joined the Browns, owner Art Modell said.

"We think he needs a lot more development," said Modell, who started talking to the Oilers about Kosar three weeks ago. "No one expects a rookie quarterback with two years' experience in college to step in . . . That's why we are not so quick to ignore (starting quarterback) Paul McDonald."

Ladd Herzeg, the Oilers' general manager, said Wednesday that eight teams have asked him about trading his No. 2 pick in the draft. He said the Oilers, who signed quarterback Warren Moon last year, will not draft Kosar.

The most enticing trade for the Oilers would be with the Vikings, who have the third pick in the draft. Minnesota General Manager Mike Lynn wants Kosar, and, in a trade including their first-round picks, the Oilers would lose nothing.

The Vikings would take Kosar, and then Houston, badly in need of defensive linemen, would likely choose Texas A&M defensive tackle Ray Childress, who is 6-6 and weighs 271 pounds.

Cleveland drafts seventh, which would not be a negative factor in any trade decisions, Herzeg said.

Modell said he would like to hear from Herzeg regarding his two trade proposals here by Friday at 5 p.m. But Herzeg said a Friday decision is just a "possibility."

"That may be his timetable, but it's not necessarily ours," Herzeg said.

In two seasons at Miami, Kosar set 22 school records, completed 463 passes for 5,971 yards and led the Hurricanes to 19 victories in 25 games.