The Italian outlet Corriere dello Sport (via interlive) claim that the Premier League duo are lining up a deal in the region of €1.8 per season.
The report goes onto state that Inter are front runners in the hunt for the Turkish international.
Erkin currently has just six-months remaining on his contract meaning he could end up being signed on a free transfer unless he extends his current deal.
The 27-year-old has also been closely linked with Liverpool after the Reds sent scouts to keep tabs on him at the Istanbul derby. Erkin rejected offers from Chelsea and Liverpool to agree a new deal with Fenerbahce back in 2014 according to the Mirror.
The former Galatasaray man has one goal and eight assists in all competitions for the Yellow Canaries this season.