The 28-year-old, who is out of contract in the summer, has scored eight goals for the Minstermen this campaign in their first year back in the Football League.
He caught the attention of a number of clubs last year and could still be the target of further interest before the January transfer window shuts on Thursday night.
Walker remains committed to the Minstermen, but is keen to test himself at a higher level.
"Obviously I'm hungry to play and prove myself at the highest level possible," he said.
"But I'm a York City player and until I hear otherwise I'm 100 per cent focused on helping us get into the play-offs."