Rice has been one of Lampard’s top targets since last summer and the Chelsea manager pushed to land the midfielder in the previous transfer window.
Ultimately, after a summer of heavy spending Chelsea were not prepared to meet West Ham’s £80m asking price for Rice and a deal was put on hold.
Lampard still wants the midfielder, but the Hammers are now in a stronger position and the 22-year-old is unlikely to burn his bridges with West Ham to push through a move.
And it has been claimed that Chelsea’s interest in the midfielder might not outlast Lampard if he leaves the club.
The Chelsea manager is under pressure following a run of poor results and there are suggestions that the club are already looking for replacements.
Lampard has been the main driving force behind Chelsea wanting to sign the West Ham star and is still pushing to take him to Stamford Bridge.
But there are no guarantees that Chelsea will continue their pursuit to bring their former academy player back if Lampard is sacked.
West Ham are under no pressure to sell and are almost guaranteed not to let him go in the ongoing window.