The player, known to be rated by City Chairman Ray Ranson, is available to leave Elland Road on a fixed fee but has yet to receive a bid from any club.
However, the CT is reporting that Beckford is warming to the prospect of a move to the Ricoh Arena with a source saying: "Jermaine considers Coventry to be a club that is going places. "It has a good stadium, good crowds, a good owner and good manager, so everything is there and he definitely considers it to be a top end Championship club."