Southampton, Nice and Celtic have all been linked with Roberts over the past week.
French outfit Nice are thought to be keen to take him to Ligue 1, but Southampton’s offer of Premier League football is a tempting one.
Roberts spent last season on loan to Celtic in Scotland and is now looking to decide on the next step in his career as he looks to further develop his game.
The Fulham academy-graduate is unlikely to make the grade at Pep Guardiola’s Manchester City this season, leaving him with the chance to go out on loan.
Southampton have made two additions to their squad this summer, with Jan Bednarek and Mario Lemina – club-record – signing so far.