The 27-year-old former West Ham defender was released by the Hammers in March and joined up with Leeds at their Thorp Arch training ground.
"He's training with us," Grayson told the club's official website. "He is available and we have given him the opportunity to train with us. He looked fit and strong, he's got a bit of work to do but we'll see how it goes.
"He's spent time doing his re-hab and we'll give him the opportunity to get fit and really impress. There is no timescale, it might be a week, it might be a month. We'll see how he is when he gets fit and ready to play and we'll take things from there."
Davenport is a former England U-21 international, who cost the Hammers £3m when he joined them from Tottenham during the summer of 2007.
Davenport spent a spell on loan at Sunderland and has also been loaned out to Watford. The centre-back started his career at Coventry and has also played on loan at Southampton and Norwich.
Source: PA
Source: PA