La Salle will host Duquesne (8-19, 1-12) and George Washington (12-13, 6-6), then visit St. Louis (21-5, 10-2).
Temple will host Detroit (18-10 entering Tuesday) and Rhode Island (8-18, 3-10), then visit Fordham (6-22, 2-11) before welcoming Virginia Commonwealth (22-6, 10-3) to the Liacouras Center.
Drexel (11-17, 7-9 Colonial Athletic Association) must win its conference tournament to earn a spot.
It's also likely that St. Joseph's (15-10, 6-6) will have to win the A-10 tournament to earn a berth, although a 4-0 finish in the regular season and a berth in the A-10 final could make things interesting.
St. Joseph's visits St. Louis on Wednesday, before home games against Fordham and Rhode Island, and a road game against Charlotte (18-8, 6-6) to end the regular season. Charlotte lost at home to Temple by 20 points on Sunday afternoon.
ESPN bracketologist Joe Lunardi believes that Villanova, La Salle, and Temple will get in. Before Tuesday's games, La Salle's ratings percentage index was 40, Temple's was 42, and Villanova's was 54.
"I think more things can go right for the three than can go wrong," Lunardi said Tuesday.
Lunardi acknowledged that Monday's 66-65 loss to Seton Hall left Villanova with little margin for error.
"Villanova has enough really good wins to withstand what was a crippling loss," he said, citing home victories over Syracuse, Louisville, and Marquette, and a road win over Connecticut.
In Lunardi's latest rankings, La Salle, Temple, and Villanova are barely in. There are 37 at-large teams, and Lunardi has La Salle 33d, Temple 34th, and Villanova 36th in the at-large pool.
Jerry Palm of CBSSports.com has La Salle and Villanova in as 11th seeds, and Temple in as a 10.
According to Lunardi, at the minimum, Villanova likely will have to split its final two regular-season games - both against teams ranked in the top 25 - and not lose to a lower-ranked team in the Big East tournament.
Temple likely has to go 3-1 and La Salle 2-1 in the regular season and also not lose to lower seeds in the A-10 tournament.