Victor Gotbaum has become an inveterate traveler in the last six months.

Like a presidential contender, Gotbaum, the most powerful union leader in New York City, has been admiring the sights in states that never attracted him before.

For the moment, he is not a declared candidate for anything. He is executive director of District Council 37 of AFSCME (American Federation of State, County and Municipal Employes), the second largest arm of the AFL-CIO, with more than one million members.

But many consider inevitable Gotbaum's challenge to Jerry Wurf, AFSCME's leader, at the union's national convention next summer. If he does declare his candidacy, a personal feud between the two men could turn into an ugly political fight.

"Wurf is getting sicker every day," Gotbaum said last month from Colorado, where he was heading a seminar on corporate responsibility at the Aspen Institute for Humanistic Studies. "He has set up a curtain of fear around him. He has an unstable personality and is incapable of running the union. There is a terrible turnover under him. We're a disgrace within the labor movement.

"This is a union of local government employees. It should be built up on a local basis. Wurf has centralized it from Washington. He has a need to take over. We've been worked over by Washington instead of working with Washington."

Wurf countered: "There are no substantive issues separating us. At the worst, we have a personal deiagreement. At best, we have someone interested in doing some social climbing.

"This is not the Victor Gotbaum I used to know. He has gotten a taste of the good life with Felix Rohatyn [a New York financier with whom Gotbaum has become friendly] in Southampton, and he's bored with New York. He now has a taste for the glories of Washington."

As the head of Council 37, Gotbaum presides over about 120,000 AFSCME members in the New York City area - more than 10 percent of the national membership. The position provides an excellent power base from which to launch a fight.

Gotbaum has been skirting the fringes of national recognition since 1975, when he played a pivotal role in helping New York City avoid financial disaster. "He's getting the image of a labor statesman," said Norman Adler, his political aide.

In limiting the pay increases for his members during that crisis, though, he was accused of caving in to management. "I was troubled by what happened," Wurf said. "I opposed him at the time, but I didn't come out publicly. But I was distressed to see the bankers come out of that thing whole."

It was during that period that Gotbaum became friendly with Rohaty, then the chairman of the Municipal Assistance Corp., a partner at the prestigious financial house of Lazard Freres, and what Wurf describes as "one of them." Gotbaum recently served as best man at Rohatyn's wedding, fueling Wurf's charges that Gotbaum has gone soft on management.

Wurf has one of the great success stories in union organizing. Since he assumed leadership of AFSCME in 1964 (strongly supported then as an underdog challenger by Gotbaum), the union's membership has risen from about 240,000 to more than a million. He is a major figure in the labor movement, a man who was summoned last month to Camp David to confer with President Carter. "I have what he wants," Wurf said, referring to Gotbaum.

Gotbaum's forays into half a dozen states in the past months to meet with AFSCME dissidents have angered Wurf and his people. All but one of these meetings have been secret, according to Adler. John Harvey, director of communications and education for Massachusetts State Council 93, had no idea, for example, that Gotbaum had even been in the state.

"We were there, but we don't take out ads for the meetings with the people who are critical of the national president," Adler said, adding that all of the meetings have been at the invitation of local members.

Wurf, for his part, injected himself into a recent dispute in Gotbaum's backyard. At issue was the in-house investigation of the president of a hospital workers local under Gotbaum's control for alleged discrepancies in the use of union funds. Both Wurf and Gotbaum charge political interference by the other in the investigation, which is now pending in the district attorney's office.

Wurf and Gotbaum, both strong, abrasive, street-smart men, already are attacking each other in sharply personal terms a year before the union election. Both are survivors But there is room for only one of them at the top. CAPTION: Picture, Victor Gotbaum: "the image of a labor statesman."