The 31 year old has fallen down the pecking order at the City of Manchester Stadium following the arrvial of Emmanuel Adebayor, Carlos Tevez and Roque Santa Cruz at the club, and has struggled with injuries recently.
Benjani’s former club Portsmouth were rumoured to be interested as well, but he is now expected to undergo a medical at the KC Stadium some time today ahead of Tuesday’s transfer deadline.
Hull boss Phil Brown is looking to strengthen his forward line further after both Kamel Ghilas and Jozy Altidore both signed on recently.
Meanwhile, defender Michael Turner is rumoured to be on his way out of the club this week, with Sunderland’s Nyron Nosworthy mentioned as a possible replacement.
“There have been two or three clubs who have made quite substantial bids and they are getting towards our valuation,” Brown told the Hull Daily Mail.
“I am hoping we can hang on to him but, if we don’t, we will have to try and get better in the camp.
“The problem is we are a bit close to the deadline.”