Adebayor has been looking for a new club since leaving Crystal Palace at the end of last season, and is eligible to sign terms with a team outside the window as he is a free agent.
However, Moyes does not envision the ex-Togo international arriving at the Stadium of Light despite Sunderland's winless start to the new Premier League season.
"We were offered Adebayor probably about four or five weeks ago," Moyes told reporters.
"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."
Sunderland will continue their search for a first league win of the season against Adebayor's former club Palace on Saturday.