Sporting Director Gary Holt will be in charge for the remainder of this campaign and will also head up the search for a new manager to take over.
Here, we look at 20 names from the likely to the unlikely and give our verdict on the chances of seeing them in the dugout at The Falkirk Stadium.
17. Ian Cathro
His last move in to management didn't work out too well but he knows how to fit in to the model of working alongside a sporting director/DoF so it's not outwith the realms of possibility. Verdict: Unlikely Photo: Lisa Ferguson
18. Gary Caldwell
Out of a job since leaving Partick Thistle and has good experience from managing in England but his stock plummeted after a disastrous run at Firhill. Verdict: Unlikely Photo: Michael Gillen
19. Martin Canning.
The 39-year old had a good few seasons with Hamilton and took up a job as Head of Coaching at North Kelvin Sports Development Group after departing New Douglas Park. Verdict: Unlikely Photo: John Devlin
20. Russell Latapy
We would all love to see this become a reality but, even if Falkirk were to approach the club legend, ask yourself... would you leave a job in Barbados for Scotland? Verdict: Unlikely Photo: Michel Gillen