Noble has made five Premiership appearances this season, and was also a part of the play-off-winning squad last year.
Taylor is also looking at ex-England Under-21 right winger Matt Piper. The former Leicester player has been released by Sunderland, who paid £3.5million to sign him from the Foxes in 2002. He could secure a deal with City if he proves his fitness after struggling with injury problems.