WEST PALM BEACH, Fla.—President Donald Trump is poised to enter the new year with the Russia investigation still unfolding, but his legal team reasserted Monday that the parts involving the president would conclude quickly.

Attorneys for the president had at one point maintained the investigation led by special counsel Robert Mueller into alleged Russian interference in the 2016 election would wrap up by year’s end, if not sooner. More recently, as Mr. Mueller’s team secured indictments and guilty pleas, they have said the date could stretch to the end of January.

In an interview Monday, Jay Sekulow, a member of the president’s legal team, stood by the prediction that the part of the inquiry involving Mr. Trump would end soon. Still, he avoided any mention of specific dates.

“I know we, collectively, the lawyers, are looking forward to an expeditious wrapping up of this matter,” Mr. Sekulow said.

A spokesman for Mr. Mueller’s office declined to comment.