The Scottish Professional Football League board has been in discussions with clubs and relevant stakeholders aimed at finding a satisfactory solution after the Scottish Government imposed a limit of 500 spectators on upcoming sporting events for up to three weeks from Boxing Day, in a bid to help slow the spread of the Omicron variant of coronavirus.
Ten out of 12 top-flight clubs are hopeful of bringing the top flight's winter break forward and postponing the post-Christmas fixtures to allow supporters to attend at a later date, although there are several logistical issues to deal with in this regard. A statement from Motherwell indicated a decision would be taken by the SPFL on Wednesday.
One option being explored is to play the Boxing Day fixtures as normal, then postpone the other two matchdays that were scheduled before the winter break.
Neilson - who has been preparing his team to face Ross County on Sunday - reckons this would help ease the fixture rescheduling issue while also potentially allowing supporters to attend two of the three games currently in question.
"For me, football is about the fans," he said. "We have to get them in as much as we can.
"In relation to this weekend, the decision has come so quickly. I understand the dynamics of trying to find dates to fit the games in, so it's a big decision to make. The sooner we get a decision the better, so we can plan.
"(If) the games go ahead on Boxing Day and then we bring the winter break forward, I think that would probably be the preference for most teams because it allows us to get the fans back in for two of the games."
Neilson also confirmed that Hearts are on the verge of cancelling plans to go on a warm-weather training trip to Spain during the January break.
He said: "We haven't made a full decision on it but it looks very unlikely we'll go. With everything going on in society, we have to be respectful of that. We could go, we have permission to go but we've made a decision that we're not going to go. That just needs to get clarified."
Livingston manager David Martindale called for player welfare as well as fan concerns to be taken into account regarding the decision over whether to proceed with the three post-Christmas fixtures.
Martindale told BBC Radio 4's Today programme Livingston were "100 per cent" looking for games to be postponed.
He said: "I think it should come down to the clubs but ultimately we've got commercial contracts and there's commercial obligations so I imagine there's a lot more stakeholders than just the football clubs that are going to be able to make this decision.
"I've spoken to a lot of my players, I spoke to players at other clubs and everybody is kind of of the same opinion that they would rather not play the fixture than play it in front of 500 fans, but that's just looking at it from a fan point of view.
"You've also got to look at it from a player welfare point of view and stopping the spread of Omicron."
Hearts, St Johnstone, Dundee and Dundee United confirmed on Wednesday that they backed plans for an accelerated winter break after Celtic, Hibernian and Motherwell gave their public backing to the idea on Tuesday.
The Premiership is due to shut down for three weeks following the clash between Hibernian and Hearts on January 3, with top-flight teams returning to Scottish Cup action in the fourth weekend of the year.
Talks on an accelerated winter break would have to include broadcaster Sky Sports, while the SPFL needs to find wriggle room in an already-crowded fixture schedule if the festive games are postponed.
However, Motherwell chief executive Alan Burrows claimed that Sky's input was not pivotal.
"We have games on Sky that are regularly postponed," Burrows told BBC Radio Scotland.
"Clubs need to recognise Sky's role in this. My understanding is that the Sky contract is for x number of games that they get to pick based on the parameters that exist within the contract. But there isn't anything that says x games have to be played on x date."
With some clubs undergoing significant Covid-related disruption to their playing squads, postponements of some festive games might be taken out of the SPFL's hands.
Humza Yousaf, Cabinet Minister for Health and Social Care, told Sky Sports the restrictions would be under "regular review" and that the Scottish Government "won't keep them in place for a minute more than they have to be".