The Daily Mirror is claiming that the east London club are keen on a move to try and bring the England international to the London Stadium for the second half of the current campaign.
The same story claims that Hammers boss Manuel Pellegrini is keen to bring the 22-year-old across London in the new year to bolster his options in the middle of the park.
However, the report says that Sarri has “ruled out” the possibility of Loftus-Cheek being sent out on loan for the second half of the campaign even though his playing time in the Premier League has been limited.
Loftus-Cheek has been earning praise for the solid performances he has produced when called upon by new Chelsea FC boss Sarri this season.
The midfielder, who spent last season on loan to Crystal Palace, has scored four goals in all competitions so far.
Loftus-Cheek is yet to start a Premier League game this season and has only made three appearances from the bench in the top flight so far.
However, he has scored four goals in his last three outings for the Blues, including a superb hat-trick in Chelsea FC’s 3-1 win over BATE Borisov in the Europa League on 25 October.
Loftus-Cheek will be hoping to be involved when Chelsea FC take on BATE Borisov away from home in the Europa League on Thursday night.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news