The left-back is expected to start for England in their World Cup qualifier in Moldova on Friday following an injury to Ashley Cole, and he is keen to reach the highest level he can in club football.
The 27-year-old was linked with a move to Manchester United during the summer, but the former Wigan Athletic player says that he does not plan to leave the Toffees.
"You want to get to the highest level you can and I keep doing my best in the hope that it comes," Baines said. "The main thing at club level is Champions League which is always going to be an aim. If you can do that it strengthens your chances at international level.
"There have been different bits in the last two or three windows, although there was probably a little bit more this time. There's nothing you can do but get on with your job. We're very blessed to do this job so I just stayed focused on that.
"You can't affect it anyway. It was mentioned that often I got puzzled by it because I'd heard nothing."
Everton currently sit sixth in the Premier League.