There was no immediate confirmation from the authorities in Mauritania, where Senussi was arrested at Nouakchott airport on Friday after arriving on a flight from Casablanca in Morocco, using a false passport.
Earlier, speaking to reporters after meeting Mauritanian leader Mohamed Ould Abdel Aziz in Nouakchott, the Libyan vice-premier said only that the president had "promised something positive" in regard to Libya's request.
Senussi, Gaddafi's feared former right-hand man, is also wanted by France and the International Criminal Court in The Hague.
Libyan Deputy Prime Minister Mustafa Abu Shagour, leading the delegation, said on Twitter after talks with Mauritanian President Mohamed Ould Abdel Aziz on Tuesday that Aziz had given his consent to Senussi's extradition and he would "soon be in a Libyan prison."
Mauritanian sources differed.
"No commitment of any kind whatsoever has been given in this case," an official source told Reuters.
Another source close to the issue said: "At this stage no commitment has been given by the Mauritanian side, it looks like wishful thinking by the Libyans."
Earlier, a security source in the ex-French colony, which is heavily dependent on foreign aid, said that other countries should also have a say in the fate of Senussi, who had been the last senior Gaddafi regime figure still at large following the dictator's overthrow and death in an uprising last year.
The source declined to elaborate but several rights groups have said they doubt whether Senussi, 62, would get a fair trial in Libya and that he would be better transferred to the ICC to face charges of crimes against humanity.