The 28-year-old came off the bench for his first appearance since September 18 to change the game at Dens Park, scoring the only goal in front of the Hearts fans in a 1-0 victory over Dundee.
Walker is out of contract next summer and Livingston and St Johnstone both want him on loan. Others may be tempted to put in a cut-price offer when the January transfer window opens in less than two weeks.
But Neilson explained: “It's a decision that me and Jamie need to come to. I'd like to keep him, but I have to respect that the age he's at, he needs to go and play. We'll see how it goes in the next couple of weeks. We'll have a chat and see what he wants to do, because it will probably come back to that.”
Walker provided the spark that was needed, a Hearts team missing Liam Boyce having dominated possession against an injury-ravaged Dundee side without creating any real opportunities.
Neilson said he was delighted for Walker and added: "He's a good player. He's a Hearts man through and through. You know when you put Jamie on, he's going to give you everything, so I'm just delighted for the kid.
“He's not played for a while and to get the winner in front of the Hearts fans is great.
"Jamie has found it hard to get in because the players that have been in those positions have been playing really, really well. He's just had to bide his time. I thought him and [Aaron] McEneff did well when they came on.
“We brought Jamie on because he's got that quality in the final moment and, especially in the second half, we pinned them in a bit in really good areas and we need somebody with that wee bit of magic. Thankfully he produced it.
"We're delighted to get the three points. It's always a tough place to come and Dundee, although they had a number of injuries, put out an experienced team. Although we controlled a lot of the game, we didn't create many clear-cut chances - but the one we did we took.”
Neilson said Stephen Kingsley is in a protective boot after limping off with a shin injury and the prognosis is not good. Boyce, however, was left out as a precaution after feeling his troublesome calf in training
Asked how the defender is, Neilson replied: "Not great. It was a tough one on him. It was a tackle that has come right on his shin. He's in a boot now so we just need to see how it is in the next couple of days.
"Boyce was more of a precaution. He trained Thursday, he felt a bit tight and he came in yesterday and we rested him. This morning it was still a bit tight and we felt we could rest him for next week.”