The 28-year-old is out of contract in the summer and has barely featured this season, but came off the bench to score the winner at Dundee on Saturday on his first appearance since September 18.
Hearts head coach Robbie Neilson said he would like to keep Walker but can’t guarantee regular first-team football and explained that the decision will be primarily down to the player himself.
Walker made a decisive impact as a substitute against Dundee, but it was only his third appearance in the league all season, all of them from the bench.
Walker said: “I’m getting a bit older now. I’m not as young as I used to be and I want to play football. But if I’m going to get more opportunities like this then I’d be delighted to stay here.”
Walker revealed that he has spoken to Neilson about getting more opportunities.
He said: “Yeah I’ve spoken to him quite a lot. We’ve got a good relationship. It’s always hard when you’re not playing but the boys have been doing well.
“We’re flying near the top of the league which means you just have to wait for your opportunity. I got that on Saturday and hopefully that’s placed a thought in the gaffer’s mind.
“I’m always confident in my own ability. If I get opportunities to play I’ll always do my best and back myself to score.”