The Hammers are looking to bring in a top-class defensive midfielder in the next transfer window and are scouring the market for options.
Frank Lampard wanted Rice at Chelsea last summer and there were suggestions that the manager’s departure meant that the West Ham star was no longer a target.
But Chelsea are still claimed to be interested in the midfielder with Thomas Tuchel also keen to take him back to west London.
However, the Blues are aware that prizing Rice out of West Ham is likely to be difficult and it has been claimed that they have laid their eyes on Tchouameni as an alternative.
The 21-year-old defensive midfielder joined Monaco from Bordeaux last summer and has had a solid first season at the club.
He was a regular in the starting eleven and his performances have piqued the interest of Chelsea ahead of the transfer window.
The Blues are likely to make move for him if they fail to lay their hands on Rice this summer.
Tchouameni has a contract until 2024 with Monaco and the club are likely to try and resist temptations to sell him after just one season.
