City are not however, the only team being linked with the Spanish international. Turkish giants Fenerbahce have been keeping tabs on Fabregas with the view to make an offer in January according to AMK.
Per the source, the Yellow Canaries will push for a permanent move or a loan until the end of the season promising the 29-year-old first-team football until the end of the season.
Fabregas has played just 87 minutes of Premier League football this season under Antonio Conte and the Italian manager is not keen on the experienced playmaker.
Chelsea signed Fabregas for £30 million from Barcelona in 2014 and he does have another three-years left on his contract.
Fenerbahce have yet to confirm an interest in Fabregas and a source close to the club revealed to Turkish-football.com that the Yellow Canaries have not made an enquiry for the Blues midfielder has not been made as of yet.
City would be able to outbid Fenerbahce but it remains to be seen whether Chelsea would be keen on selling Fabregas to a rival in the title-racemic-way through the season.