Loftus-Cheek impressed on loan at Crystal Palace last season, with his performances for the Eagles earning him a place in England's World Cup squad.
The 22-year-old further enhanced his reputation by helping the Three Lions to the semi-finals in Russia, but he faces stiff competition for places at Chelsea with Jorginho, N'Golo Kante, Cesc Fabregas, Ross Barkley, Mateo Kovacic and Danny Drinkwater also available to Maurizio Sarri.
Loftus-Cheek is still able to join a foreign club on loan despite the English transfer window closing last week, and Bundesliga outfit Schalke are understood to be the first to have registered an interest, having lost Max Meyer during the summer.
However, The Guardian reports that the England international is determined to work his way into Sarri's first-team plans this season and will reject the chance to move abroad as a result.
Barkley was selected as the third central midfielder alongside Jorginho and Kante for Chelsea's season-opening win over Huddersfield Town, although Loftus-Cheek did make a 22-minute cameo off the bench.