The Senegal international looks to be on the way to the KC Stadium where, should he sign, he will link up with Abel Hernandez whose move to Hull from Palermo has been completed.
Diame, who worked under Hull manager Steve Bruce when the pair were at Wigan, has made 79 appearances for West Ham following his move from the 2013 FA Cup winners two years ago.
But the France-born midfielder has only started one game for Sam Allardyce’s men this season, the penalty shoot-out defeat to Sheffield United in the Capital One Cup last week.
Hull manager Steve Bruce has earmarked the recruitment of a midfielder to bolster his squad before the end of the transfer window and has been linked with a move for Manchester United’s Tom Cleverley.
But the England midfielder appears to be edging towards a switch to Aston Villa, prompting a late move from Bruce for Diame.
The former Rayo Vallecano player has moved further down the pecking order at Upton Park following the summer arrivals of fellow battle-hardened midfielders Alex Song and Cheikhou Kouyate.