The 33-year-old Potters captain is out of contract in June but is in talks to terminate his deal early.
Centre-half Shawcross, who arrived at Stoke from Manchester United in 2007, hopes to secure an exit in order to head for pre-season training at Inter on February 22.
“There is interest from an MLS club, discussions are open and forthright on that but nothing is concluded at this minute in time.
“To be fair to the player, Ryan has expressed the interest if the opportunity is given and we as a club have to recognise what Ryan has given us in terms of service.
“At this minute in time we didn't think it was the right thing to involve him.
“He's fit now but he's had bad luck over the last 18 months with injury and until this situation is resolved, we just have to be careful at this minute in time."