The Scotland international initially nailed down a spot in Daniel Farke's first XI, starting four of his side's first five Premier League fixtures since arriving at Carrow Road.
However, Gilmour has been an unused substitute in his side's last three Premier League encounters, two of which saw Norwich earn their first points of the season against Burnley and Brighton & Hove Albion.
As a result, The Express speculates that Chelsea director Marina Granovskaia could consider recalling Gilmour over the winter, especially with Farke insisting that Norwich are not under any "pressure" to give minutes to loan players.
The report adds that it 'would be no surprise' to see Gilmour back at Stamford Bridge in January, where he has already made 22 appearances for the Blues' first team.
The 20-year-old's deal with Thomas Tuchel's side is due to expire at the end of the 2022-23 season.