Reports have suggested Arsenal boss Arsene Wenger was weighing up a move for Guzan after being impressed by the American's performances.
The 29-year-old has established himself as a key player in Paul Lambert's side after he initially found himself released by the club in the summer of 2012.
Lambert brought Guzan back to the club after replacing Alex McLeish as manager and made him No.1 keeper in place of Shay Given.
Guzan, who signed a new four-year deal over the summer, admits he was flattered to be linked with other clubs, but is determined to stay at Villa to repay the faith shown in him by Lambert.
"Aston Villa, they've stuck by me, especially the manager, [Paul Lambert]," said Guzan, who was speaking to ESPN.
"He's given me a chance to play consistent football in Europe. It's always nice when you're linked with other teams, but for me, I'm very happy at Aston Villa."
Villa narrowly avoided relegation last season, but they have impressed so far this term beating the likes of Arsenal and Manchester City and Guzan predicts a bright future for the Midlands outfit.
"It's a club that I think is definitely on the rise, and it's something I want to be a part of," added Guzan.