Barry still has two years of his contract left to run and is due a testimonial, having signed professional forms for Villa in February 1998.
Barry, who has been capped 17 times by England, told BBC WM: "It's certainly flattering to be linked with them [Chelsea and Liverpool], but I'm enjoying my football here.
"There's still so much to play for at Villa and there's no reason to be sidetracked by anything else."