Brentford will allow Allen to leave
Tranmere and Northampton are believed to lead the chase to appoint Allen, who has told the Bees he wants to leave the club, as their new boss.
Allen has another year left on his contract at Griffin Park, but will be allowed to leave if a rival club pays compensation to Brentford.
A statement read: "While Martin Allen is still under contract to Brentford, he has now made it clear to us he does not wish to be the manager for next season.
"After prolonged discussions with Martin, we have accepted this position and put in place a search for a new manager.
"If other clubs seek our permission to talk to Martin, we are prepared to agree to this as long as Brentford receive the appropriate compensation if he is appointed."