U.S. Senate Democratic leader Harry Reid said on Thursday he believes President Barack Obama will nominate a replacement for the late Supreme Court Justice Antonin Scalia in a little over three weeks.

"I think it will be a little over three weeks," Reid said in an interview on MSNBC, adding that he spoke to Obama about the nomination on Thursday.

Vice-President Joe Biden said in an interview broadcast on MSNBC he would be deeply involved in advising Obama but that he had no desire himself to be named to the high court. He said the president has sought his advice but they had yet to discuss potential candidates.

A fierce political fight is brewing as the Democratic president prepares to name a successor to conservative Scalia, who died on Saturday. Obama's nominee could change the court's balance of power, as Scalia's death left it with four conservative and four liberal justices.

Many Republicans, led by Senate majority leader Mitch McConnell, have said the seat should remain vacant until Obama's successor takes office next January so voters can have a say in the selection when they choose a new president in the Nov. 8 election.