Moore has been in stunning form this season for Brentford and has been instrumental in their push for promotion from League One.
The 22-year-old has been a virtual ever-present in Uwe Rosler's side and has kept 13 clean sheets so far this term.
Moore has been winning rave reviews for his performances and former England goalkeeper David James has tipped him as a future England keeper after coming up against him while at Bournemouth this year.
Manchester United have been credited with an interest in the athletic shot-stopper, after sending scouts to watch him in action, while the likes of Newcastle and Sunderland are also thought to be admirers of Moore.
Championship promotion hopefuls Hull City and Nottingham Forest are also keeping tabs on Moore as they weigh up moves for the former Southampton trainee.
Moore is flattered by the reported interest in his services, but insists he is fully focused on helping Brentford win promotion to the Championship.
"It is obviously flattering to be linked with clubs in the Premier League and Championship, but all my focus is on helping Brentford secure promotion," Moore told Sky Sports.
"I am happy at Brentford and I want to keep playing regularly so I can continue my development."