Brown, 28, has 18 months remaining on his current contract with the Scottish champions and there have been suggestions that the midfielder may want to move south of the border when his deal expires.
However, the 36-time Scotland international claims that his heart belongs to the Hoops.
"I don't see why I would swap winning trophies, winning leagues and playing in the Champions League," Brown told reporters. "I know people from England will want to go back home and that's understandable.
"But for me this is a great club, my family is here and I'm not going to beat the occasions I get in the Champions League.
"Everyone knows that England is where the money is. But if I put my heart before the cash signs, it's Celtic for me. I've been here for nearly seven years now and I can see myself staying for a lot longer."
Brown has made 248 first-team appearances for Celtic since signing from Hibernian in May 2007.