The 35 year-old stopper has racked up almost 200 games for the Milelrs but this season has been relegrated to second choice by boss Andy Scott after the loan signings of Conrad Logan and Rhys Taylor.
But Warrington says he's happy to fight for his place in the team and doesn't want to leave.
“Every player wants to play football, but when you have an affinity with a club and get on with its people and the supporters, you like to stay,” he told the Advertiser.
“I had a great affinity with Doncaster Rovers. I had eight fantastic seasons there and I've had five here and I'd be happy to add a couple on, but that is not my decision. I want to be play first team football, not reserves, but the other side of it is that I love this club as well.
“Everyone knows how I feel. When you're a local lad, you want to see the club progressing. It's going in the right direction and I want to be part of that and after four years at Don Valley, it would be great to get to the new stadium and play in there. Wherever I fit in, if they use my experience behind the scenes with the younger lads or something like that, I'd consider it. There is a great goalkeeping coach here in Andy Dibble and I'm not looking to pinch his job, because he's been great with me. But even if I came back at some point in future to do something like that, it would be nice.”
Warrington is always welcomed by Millers fans for his commitment and ability to pull off match winning saves and made a couple of good stops against Bristol Rovers last weekend. However he's set to warm the bench again at Barnet tomorrow when Taylor returns from an arm injury.
He adds: “The supporters have been absolutely fantastic with me and when I came back in earlier in the season I think I put a bit too much pressure on myself. I was trying too hard and when you do that it detracts from other things in your game. Because you have the supporters behind you, you want to prove to them that you can still play well and I heaped pressure on myself, whereas on Saturday I came in relaxed and I enjoyed it, apart from the result. When you return, you want a clean sheet. I was pleased with how I did but ultimately we lost the game.
"Rhys has done really well but I want to play. There might be some other opportunities between now and the end of the season to play in the side so I'll just stay positive. We will have to wait and see what happens."