The 19-year-old has impressed for the Scottish side this season and Sky Sports reports that a number of clubs are keeping tabs on the youngster.
Manchester United chief scout Martin Ferguson reportedly watched Allan in action for Dundee United in their clash with Dunfermline last month. Allan did not make it off the bench in that game.
Allan is reportedly yet to agree a new contract at Dundee and his current contract with the club is set to expire at the end of the season.
