The 21-year-old is currently on loan with Scottish champions Celtic, as he prepares to face Motherwell in the Scottish Cup final at Hampden Park on Saturday.
He will return to his parent club after the end of the season, and the report claims that West Ham and Leicester are expected to lodge bids for the £15million-rated attacking player after that.
Celtic are also willing to keep the highly talented left-footed trick-star with them, but the Bhoys can only sign him on yet another loan deal.
Roberts has made only 18 appearances for Celtic this season, with injuries preventing him from playing more. However, his overall loan tenure with Celtic has been superb – he has been involved in 44 goals (scoring 18) – and he is loved by the fans.
He still has two years left on his deal at Manchester City and will be looking to impress Pep Guardiola during the pre-season. Roberts personally prefers to play in the Premier League and should look to move if West Ham or Leicester come up with a good offer.