Adebayor is currently a free agent having left Crystal Palace at the end of last season, although the 32-year-old forward is actively looking for a new club.
He was in talks with French outfit Lyon before a move fell through, and now it has come out that the Black Cats were offered the striker – who has 97 Premier League goals to his name following spells with Arsenal, Manchester City and Tottenham.
Speaking prior to Sunderland’s game against another of Adebayor’s former clubs, Palace, Moyes said: “We were offered Adebayor probably about four or five weeks ago.
“I didn’t do anything about it then and I don’t expect to be doing anything about it just now unless something dramatically changes.”
Moyes has already used the free market to strengthen his struggling side, bringing in former Everton forward Victor Anichebe at the beginning of September.