Brown, who joined The Hoops from Hibs for £4.4million in the summer, says he would not have been interested in a move south even if it had been put to him.
"I don't know anything about it, but I'm delighted to be at Celtic and I definitely see my myself playing here for the next few years," Brown told The Herald.
"The chance of playing in the Champions League was why I signed for Celtic and I'm so glad we got through the qualifier," he added.
"The atmosphere at the (Spartak) match was unbelievable, along with my Scotland debut, that was the highlight of my career."
Meanwhile, Newcastle United were last night linked with plans of making a January offer for the dynamic Brown.