Doku has emerged as a big target for both clubs in the final weeks of the summer transfer window.
West Ham are more advanced in the negotiations and have tabled a bid, which is claimed to be less than the £50m that Rennes want before agreeing to sell him.
Manchester City remain confident that they will be able to beat the Hammers to the signing of Doku in the coming days.
However, both clubs have lined up the same alternative target if either of them fail to land Doku.
It has been claimed that Eze is the player both West Ham and Manchester City have identified as the backup to Doku.
The club who fail to land the Belgian are expected to make a move to snare Eze away from Crystal Palace.
The Eagles have succeeded in convincing Michael Olise to snub a move to Chelsea and sign a new contract.
They are in talks with Eze over a new deal as well and Roy Hodgson has stressed the importance of holding on to him.
