A Palestinian minister has visited Marwan Barghouti, a leader of the main Palestinian political faction, Fatah, in an Israeli jail on Friday.
Israel jailed Marwan Barghouti for complicity in a string of murders
Palestinian Authority minister Kadura Fares met Mr Barghouti to discuss a successor to Yasser Arafat.
Mr Barghouti's lawyer told the BBC he had decided to run in the election.
But a formal announcement has yet to be made on his bid, which may split support for the official candidate named by Fatah, Mahmoud Abbas.
Mr Barghouti's lawyer said his final decision would depend on his talks with Mr Fares.
Mr Abbas - a former Palestinian Prime Minister and the PLO leader, also known as Abu Mazen - was nominated as Fatah's candidate for the presidential elections in January.
Possible Fatah split
The BBC's Alan Johnston in Jerusalem says a contest might well split Fatah between younger Palestinians, who back the more charismatic Mr Barghouti, and the older guard, who support Mr Abbas.
Mr Abbas has already replaced the late Yasser Arafat as Palestine Liberation Organisation (PLO) chairman and is now favourite to succeed him as president.
Barghouti, currently serving five life sentences on terrorism charges in an Israeli prison, would have to run as an independent.
But it is believed that he is the most popular Palestinian leader. He is seen by many as a hero and a major figure in the fight against Israeli occupation, our correspondent says.
He has been described as charismatic and determined, and was often thought of as a natural successor to Arafat, our correspondent adds.
The nomination of Mr Abbas came at a Fatah Revolutionary Council meeting in the West Bank city of Ramallah on Thursday night.
Palestinian official Tayeb Abdel said Mr Abbas was now "the only candidate of the Fatah movement", the Associated Press news agency reported.
Our correspondent describes Mr Abbas as very much the kind of man that Israel and the West would like to see emerge as the new leader.
Mr Abbas is a moderate who has opposed the armed struggle against Israel, but he is a rather grey figure, who lacks a popular following, our correspondent says.
He adds that if indeed Barghouti does decide to run, he will pose a serious challenge to Mr Abbas.