Turkish outlet Sabah claims that the 25-year-old has attracted interest from the Premier League side after starting the 2019/20 campaign in good form.
It was his second goal of the international break, after also hitting the target in a 3-2 win away to Bulgaria on Friday.
However, the report warns that Fenerbahce are unlikely to let the striker go without a fight in January and will hold out for a large bid.
Muriqi only arrived at the Istanbul giants this summer from Caykur Rizespor for €3.5 million but has settled quickly by scoring twice in the opening three Super Lig games of the season.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.