Fans favourite Alan Archibald has been taking the team on an interim basis since the departure of Jackie McNamara and Simon Donnelly to Dundee United last month.
SportTimes understands the 35-year-old is one of the names on the Thistle shortlist, which has been whittled down in recent days after an initial flood of applications following McNamara's exit.
Former Rangers midfielder Ian Ferguson and ex Hull City boss Phil Brown have both been linked with the position, but it is Archibald who has the first chance to claim the top job.
Since being appointed as interim boss, the Jags defender has guided his side on a four-game unbeaten run as they have drawn with Irn-Bru First Division title rivals Morton and beaten Airdrie United, Hamilton Accies and Dunfermline.
And those results have kept up the pressure on the Ton in the title race.
Archibald has the overwhelming support of the Firhill squad and many players have spoken of their hope that their team-mate lands the job on a permanent basis.
The Jags hierarchy have not approached any of the final six to speak to them over the position and are in no rush to make an appointment, with Archibald and assistant Scott Paterson continuing to take the team on a day-to-day basis.
A Firhill source told SportTimes: "The board have narrowed it down to six people. They haven't approached anyone to interview them. The club has an internal shortlist, but haven't approached anyone.
"The board are trying not to put a timescale on it. There is no rush to do anything. Archie is doing a fantastic job.
"The board have sat down with Archie and told him how they plan to do things. He is aware of the process. This is the way the board want to do things just now. Archie is still the interim manager and is keen to show what he can do.
"The board are very open and honest with him and he has been the same with the board.
"With every game that he wins, it is another feather in his cap. Archie is probably favourite for the job just now.
"There is a lot going on at the club just now and a lot of work that needs done in terms of youth development and that kind of thing.
"It is not just purely managing the football team. That is 80% of it, but there are important factors regarding how we build the club and how we develop players."