The 20-year-old has spent the last 18 months on loan at Scottish Premiership champions Celtic, where he impressed with a return of 15 goals in 43 league appearances.
Brendan Rodgers's side had been hopeful of extending that deal for this season but have faced competition from a number of rivals, including Ligue 1 outfit Nice, who reportedly firmed up their interest over the weekend.
Now Roberts is said to have been offered a chance to feature in the Premier League this term, with The Mirror reporting that the Saints are also keen on his services.
The newspaper claims that the England youth international "is open to a move to Nice" but could be swayed by the prospect of playing in the English top flight.
Roberts moved to City from Fulham in July 2015 for a reported fee of £12m and has to date made three senior appearances for the side.