Andy Morrell's departure has left the Skrill Premier side looking for a new boss, with his assistant Billy Barr in caretaker charge.
The club are set to advertise the position today and Harrison has been linked, although he is contracted to TNS until the end of next season.
The former Middlesbrough, Crystal Palace and Preston North End defender, 36, has been with the Welsh Premier League champions since 2011.
He insists he's yet to be approached by the Dragons and is happy at TNS, but added he's proud to be associated to a high-profile post.
He said: "I am flattered to be linked to the post, Wrexham are a good club with a great history and are sort of a sleeping giant at that level. You realise you are doing a good job when people mention you about these jobs. It gives you a bit of confidence about what you are doing.
"I have won two league titles, a Welsh Cup and done well in the Champions League with TNS. I am more than happy here and I am enjoying it.
"Nothing has been said or done. I haven't had any contact or been approached. That said, I am an ambitious guy."
During his two-and-a-half years in charge at the Racecourse Ground, Morrell achieved two runners-up finishes.
Last year he led Wrexham to Wembley for the first time in their history, winning the FA Trophy against Grimsby Town, and then again six weeks later when they narrowly lost out on promotion back to the Football League in the play-off final.
Morrell said: "I feel it is in the best interests of both Wrexham FC and me to make a change now, so that we can all plan for the future with certainty.
"I'm disappointed with how this season has gone, as I desperately wanted to lead the club I love back to the Football League where I feel it belongs."
Morrell's depature has seen him linked with joining Shrewsbury as new boss Michael Jackson's No.2.