Leno's contract is due to expire at the end of the current season and reports claim he could leave the club following Aaron Ramsdale's arrival.
Inter have been linked with a move for the German as they look to replace the 37-year-old Samir Handanovic, according to TuttoSport.
The report adds that the Nerazzurri have identified Leno and Ajax goalkeeper, Andre Onana, as potential replacements.
Arsenal signed Ramsdale this summer from Sheffield United as a back-up to their first choice goalkeeper. They bought the 23-year-old in a deal that could end up being worth up to £30m.
However, Leno has previously admitted he had no desire to leave the club and wanted to get Champions League football back at the Emirates Stadium.
Leno told German news outlet Sport1: "I don't want to leave here, I feel good and want to be successful again with Arsenal. Arsenal are a big club, which is extremely underestimated in Germany, there are many Arsenal fans all over the world. I still have a two-year contract and hope to play in the Champions League again with Arsenal.
"It is also clear that at some point in my career I want to do something different. So far I've played for two clubs. Maybe I'll get the urge to play in another league again. Maybe in the south. But there is time, I'm still getting to the top goalkeeping age. But my focus is on Arsenal."