Ilgauskas has the option of signing for just the remainder of this season or adding extra years to the deal.
"It's just a matter of how long of a contract we'll sign," Herb Rudoy said.
Earlier in the day, Rudoy said he wasn't interested in any deals beyond this season. He wanted Ilgauskas to be an unrestricted free agent this summer. Ilgauskas, though, is contemplating signing with Cleveland beyond this year.
"It'll be resolved for sure," Rudoy said earlier in the day. "We're not very far apart. The plan is to try and get him on the plane tomorrow."
Cleveland departs Tuesday for a two-game road trip to New Orleans and San Antonio. Rudoy is still hopeful Ilgauskas will be on the flight.
Cleveland dealt Ilgauskas to Washington at the trade deadline in a three-team deal that brought Antawn Jamison and Sebastian Telfair to the Cavaliers. Monday is the first day he is eligible to re-sign with the Cavaliers under league rules.
Ilgauskas spent his entire career in Cleveland before the trade, although he never appeared in a game for the Wizards. He is averaging 7.5 points and 5.3 rebounds per game this year and is the franchise's leader in games played, blocks and rebounds. He's second in career scoring behind LeBron James and one of the most popular players in team history.
He has been in Cleveland for at least the past week working out at a suburban gym and staying in shape until he was eligible to rejoin the Cavaliers.
His return means Cleveland acquired Jamison, a two-time All-Star with nearly 17,000 points, for a 2010 first-round pick and the rights to Emir Preldzic, a second-round pick last year.