The club confirmed last week that Stephen Crainey, who had taken charge until the end of the season after the departure of Simon Grayson last November, would be returning to his role with the Under-23s.
Brown, the former Celtic captain who has announced his retirement from playing after departing Aberdeen, is the favourite to take charge at Highbury.
The 36-year-old had also spoken to Raith Rovers about their vacant role, having previously been linked with vacancies at St Mirren and Kilmarnock earlier in the season.
Brown has made no secret of his eagerness to take up a coaching role and, having spent 14 years at Celtic and won 22 trophies, he hung up his boots was with his future career in mind.
There has been no comment from Fleetwood on the rumours, with owner Andy Pilley and CEO Steve Curwood currently in Dubai to watch sister club Fleetwood United’s play-off campaign – they face Gulf United in the final tomorrow evening.
There are, however, reports north of the border that all has been agreed with Brown and that he will be confirmed as the Cod Army’s new head coach next week.
Head of recruitment James Wallace, meanwhile, has been linked with a move to Championship Preston North End in a similar role. It is understood, though, that North End are more interested in a chief scout.