It emerged last week that the West Lothian club had failed to satisfy UEFA licence requirements over their youth academy and published accounts ahead of the deadline at the end of March.
Livi face Aberdeen in the Scottish Cup last 16 on Saturday and sit fifth in the Scottish Premiership, a position which might carry a place in Europe depending on the cup winners.
But Martindale is optimistic UEFA could waive their youth academy demands if the club convince the governing body that plans are in place.
"It's still ongoing," he said. "The club are working hard behind the scenes to meet as much of the criteria as possible.
"We had five teams all set up last year, all recruited and ready to go, and then Covid hit. So it made no sense to try and get that up and running until there is a bit of clarity in what's happening with Club Academy Scotland and youth football.
"We have the coaches in place, it's just a matter of getting the green light and pushing on with that.
"But there is special dispensation for clubs due to sporting integrity. For talking's sake, if someone in the Championship won the Scottish Cup, they could get special dispensation with UEFA. We believe we fall into that criteria.
"We were in the Premiership roughly 18 months and had our youth academy ready to get back up and running and then Covid hit. So it has been really difficult to implement that.
"Hopefully if we can achieve European football - and that is still a big ask - then the sporting integrity side will come into it.
"But we very much work on individual games. We have a fantastic opportunity to go up to Aberdeen in the Scottish Cup, which gives you Dundee United at home - and we fancy ourselves against anyone at home.
"There is a lot to play for in the season, we have fifth place, potentially fourth place and the Scottish Cup at stake."
Livi are looking to bounce back from their 6-0 defeat at Celtic Park and Martindale does not feel the heavy defeat will impact them at Pittodrie.
"We take every game in isolation," he said. "When you're winning games of football it's very easy, when you're losing you have got to identify what went wrong but it's easy to identify that and take it in isolation."
The Dons have Stephen Glass in charge for the first time but Martindale believes he has already seen the new manager's impact in games during his quarantine period.
"I think the players will have that wee extra edge about them, but I do believe since Stephen was appointed, you can see Stephen's influence on the team already," he said.
"There have been subtle differences, they have changed their shape from 3-4-2-1 to 4-2-3-1. They are probably playing out from the back a little bit more and trying to get the ball down."