Hearts’ top scorer Liam Boyce hobbled off during Saturday’s 1-1 draw with Dundee at Tynecastle following a tightness in his calf.
Boyce is such a key player for the Edinburgh club and is unlikely to be risked, which would mean Armand Gnanduillet is likely to lead the line against St Johnstone on Wednesday night.
Neilson explained that the decision will lie with Boyce. He said: “Liam Boyce did a wee bit today. He didn’t train with the full team and we’ll see him again on Wednesday.
“To be honest, it will be up to Liam to see if he’s right or not.
“The big thing I spoke to him about is making sure he’s at it. We’ve got a good squad here and if you’re not and you break down you could be out for two or three weeks.
“So, the decision will come down to Liam.”
Saturday’s draw stretched Hearts’ unbeaten run to ten games, however the fans disappointment at full time was visible and Neilson admitted, there was a similar feeling in the dressing room.
“There was a disappointment in the dressing room. We knew we had the chances to win the game and we should have put it to bed.
“We didn’t do it and we lost a goal. That’s football, it happens.
“The big thing for us is we played really, really well and passed the ball well. It was probably the best we’ve played all season, but we just didn’t have that final moment.
“But sometimes you just have to accept that and move on to the next game.
“The players here know we’re playing well, we’ve got a really, really good squad, with competition for places, and we want to try to do something this season.
“We want to be up the top end of the league and we want to continue to win games.
“We missed that wee chance on Saturday. It was there for us to take and it’s a lesson we need to learn, but we move on to the next game.”
Hearts haven’t won at McDiarmid Park since November 2010 and the Hearts boss is under no illusions that his side will be in for a tough evening.
“McDiarmid Park is always a difficult place to go to,” Neilson said.
“It’s tough for all teams. Look at Rangers earlier in the season when they won 2-1 and managed to get three points.
“For us, can we go up there and can we continue our good away record, which has been very good this season? But we know it will be tough.”
The Jambos will be backed by well over 3,000 Jambos in Perth and Neilson was full of praise for the supporters.
“It’s absolutely brilliant, to be honest with you. The Hearts fans always travel in numbers and we’ve got two good away games for them.
“Hopefully we can get a good result against St Johnstone and then we’re taking about 1,000 to Aberdeen and have a good crowd up there.”
The Hearts boss will serve the second of his three-game suspension at McDiarmid Park and when asked if he had his seat sorted, he laughed:
“I’ll just wait and see where Callum puts me!
“It doesn’t really matter where I sit, to be honest with you. Gordon Forrest and Lee McCulloch can deal with it. They’ll deal with the game and I’ll oversee it.”