Chairman Ron Martin says a new boss will be in place by the end of Monday as he attempts to salvage the club's League Two play-off hopes.
And Brown - out of work since leaving Preston in December 2011 - met the Southend players at the club's training ground on Monday morning.
The 53-year-old is now believed to be finalising terms and he will take charge of the team for Friday's trip to Bradford.
Southend go to Valley Parade with six points to make up on seventh-placed Rotherham in their remaining seven games.
A Wembley date with Crewe in the Johnstone's Paint Trophy final is scheduled for 7 April, when Martin hopes Sturrock will return to lead out the team.