The Big East Conference, seeking a solution to its "football problem," yesterday extended an invitation to the University of Miami. The school's 55-member board of trustees will vote Wednesday whether or not to accept the offer.

Mike Tranghese, who has been courting football powerhouse Miami as his No. 1 priority since he became Big East commissioner this summer, said the conference does not have a commitment from the university.

"We're hopeful," Tranghese said after Big East and Miami officials met for nearly five hours yesterday in Coral Gables, Fla. "When you dance with somebody for three months, you usually wind up taking them home."

Miami President Edward T. Foote II and Athletic Director Sam Jankovich, who Saturday said his school was leaning toward choosing the Big East over a number of other suitors, declined to predict the outcome of the vote. "Until the final decision is made, any speculation . . . would be premature," Foote said at a news conference in Coral Gables.

A simple majority vote is needed to accept the offer.

Big East and Miami officials declined to talk about details of the school's possible membership until after the trustees vote. If it joins, Miami is expected to compete next season for all league championships, including men's and women's basketball. The school would be a full-fledged voting member of the Big East immediately.

Miami, a national football power, would become the Big East's 10th member and its fourth Division I-A football school, joining Syracuse, Pittsburgh and Boston College. Those schools are expected to discuss at least five football options to form an alliance with other Division I-A schools. "There would be no timetable, and we would just take our time," Jankovich said.

Under any alliance, Miami, national champion three of the past eight years, is expected to be able to continue playing a national football schedule, with five nonleague games. Tranghese considers such a a football arrangement pivotal to the Big East's long-term survival as one of the country's top basketball leagues.

The Federal Trade Commission has filed a complaint against the College Football Association's new five-year contract with ABC-TV Sports, claiming it violates antitrust laws. No matter what the outcome in the courts, conferences are expected to make their own network deals after 1996. That is a major reason for the expansion and realignment talks now gripping college athletics.

Tranghese fears that without a football alliance, the Big East could lose its football-playing members, and eventually the football powers could hold their own basketball tournament.

Thus, the makeup of the Big East's seven-person delegation that met with at least 15 Miami officials yesterday was significant. In addition to Tranghese and Georgetown Athletic Director Frank Rienzo, chairman of the league's executive committee, members of the group included the presidents of Syracuse and Boston College, and the athletic directors from Syracuse, Pitt and Boston College.

Issues such as academics, revenue-sharing, compliance and the football options apparently were discussed during the meeting. "There was a comfort level in the discussion," Tranghese said.

Previous talks mainly involved Tranghese, Jankovich and the athletic directors of the Big East's three Division I-A football schools.

Asked whether the Big East could be embarrassed if Miami rejects the bid, Tranghese said: "We're comfortable. If you involve yourself in politics and posturing, then there's a risk. We've been dancing with them for months, and there's no need to play games with them.