Virginia will not accept an invitation to the White House to commemorate its run to the national title, coach Tony Bennett said in a statement on Friday.
Bennett said logistics, not politics, would preclude Virginia from accepting an invitation.
Four Virginia players have declared for the NBA draft.
It's unclear if President Trump has formally extended an invitation to the program.
"We have received inquiries about a visit to the White House," Bennett said in the statement. "With several players either pursuing pro opportunities or moving on from UVA, it would be difficult, if not impossible to get everyone back together. We would have to respectfully decline an invitation."
The Cavs won their first national championship in men's basketball with an 85-77 victory over Texas Tech in Minneapolis earlier this month.
Since that win, stars Kyle Guy, Ty Jerome and De'Andre Hunter have all entered the NBA draft, hired agents and announced their intentions to remain in the draft. Hunter and Jerome are both projected first-round picks in ESPN's most recent mock draft.
Mamadi Diakite has also entered the draft after averaging 7.4 PPG this season. He can retain his collegiate eligibility if he withdraws by the May 29 deadline.
Under President Trump, traditional invites to the White House following championship runs have become polarizing events.
Washington Capitals forward Brett Connolly did not join his teammates at the White House after their run to the Stanley Cup last season. In 2017, Dawn Staley announced that her team would not accept an invitation to the White House after South Carolina's run to the women's basketball national title.