The 18-year-old central defender made his first-team debut last year but is now becoming a regular in Neal Ardley's first-team set-up.
Sweeney’s current deal is due to expire in the summer, and although they do have an option on him – talks over a new deal have not resulted in him agreeing terms.
The Dons now face a real battle to hang onto the highly-rated defender, who has a host of clubs ready to make him an offer.
A source confirmed to HITC Sport: "A lot of clubs are watching Sweeney, he is a very impressive."
Sweeney, an Irish youth international, is being scouted regularly by up to a dozen clubs – but the main interest is coming from the capital with Arsenal, Spurs and West Ham looking to take him to the top-flight.