Weir had been with the Gable Endies for more than two years
Former Scotland international Willie Donachie has expressed interest in becoming manager of Montrose.
The 57-year-old has previously been in charge of Millwall and is understood to be keen on working in Scotland.
Jim Weir was relieved of his duties as Links Park boss prior to Saturday's 1-0 win at Albion Rovers.
Assistant manager Kevin McGowne and captain Keith Gibson took charge of team affairs at the weekend, while the club have not commented on Weir's exit.
Having lost just one of their nine league matches, Montrose sit four points behind Third Division leaders Stenhousemuir.
Weir had been in charge of the Gable Endies for more than two years but it is understood there had been friction recently between the board and their manager.
Donachie spent most of his playing career in England, most notably with Manchester City. The defender won 35 caps in total and played at the 1978 World Cup in Argentina.
Gary Bollan, Ray McKinnon, Bobby Mann and Steven Tweed are also being linked with the manager's post at Montrose.
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