The Raith Rovers boss, who is out of contract at the end of this season, has been prominent amongst discussions around the future Bairns boss and fits the criteria to replace Martin Rennie.
Kenny Miller took interim charge for the final games of the failed League One promotion bid, but after Saturday’s 1-1 draw with Queen’s Park admitted his chances of retaining the position were slim.
He said: “Continuing the work I have put in so far is what I would love to do and from the players I couldn’t ask for anything more.
“The feeling however is that it is probably a no.”
The Bairns are hoping to make an announcement within the next week and had narrowed their search before a Daily Record report on Monday lunchtime linked McGlynn to the job.
He is in his second spell at Stark's Park and talks have been on-going over his current deal which expires this summer, but Falkirk have now moved in as they seek an experienced, steady hand to lead them out of League One at the fourth attempt.
McGlynn denied their closest promotion bid two years when his Fife side pipped the 2019-20 title on average points, making the move into the Championship by 0.34points after the season was ended early by the covid-19 pandemic.
This term Falkirk finished a lowly sixth in League One, outside the play-off positions and below fifth-placed Alloa after a season which saw three managers – Paul Sheerin, Martin Rennie and latterly Miller – take charge.