Adebayor could be set for his Tottenham debut if he completes his loan move from Manchester City in time.
Livermore would welcome the Togo striker with open arms despite the fact that he used to play for bitter rivals Arsenal.
He said: "Adebayor is a great player. He would be a great addition to the squad. Robbie (Keane) has gone now so we need to strengthen up front a bit."