The Tynecastle manager said he will let players decide if they will accept the silverware following the club’s controversial relegation last year.
"The players have done the hard yards and they will decide what they want to do,” said Neilson following Tuesday night’s goalless draw at Morton.
Hearts are due to be presented with the trophy after Saturday’s home game against Inverness Caledonian Thistle.
However, some fans want them to leave it on the stand in a retort to the Scottish Professional Football League for allowing their club to be relegated despite last season being incomplete.
On the scrappy draw in Greenock, Neilson added: “It will be a struggle when I go through it again and watch tomorrow morning. It's very difficult to play football on that pitch. Every time you pass it, the ball is bobbling all over the place.
“It's difficult to take touches and difficult to get any real quality on it. We knew that coming down here, that's why we went with two men up top. Even when we did go direct, it's very unpredictable when the ball drops down.
“We set out to win the game but it wasn't to be. We had a couple of chances but we didn't take them.
“We're at Tynecastle on Saturday and then Raith Rovers next Friday. It's two good surfaces against two teams who will open up and try to win the game. It should be two good games to finish the season off.”
The Morton manager Gus MacPherson welcomed a point in his quest to keep the club in the division.
“It’s a good point and good performance. We're frustrated it's only a point so that's a good sign,” he explained. “We couldn't ask for any more from our players.
“We had a chance very early in the game with Kalvin Orsi [who hit the post]. I think we'd have had to defend a lot deeper if that had gone in. We are in this situation which has been there for a while. We trust the players in how they're applying themselves.”