Allen resigned from the London club a day after a board meeting to decide the playing budget for next season.
No figures have been announced, but "Mad Dog" has left the club he guided to the League One play-offs in consecutive seasons.
This year they lost to Swansea City in the semi-finals, having suffered the same fate at the hands of Sheffield Wednesday last time.
BBC London are reporting that he has held talks with Tranmere, who accepted the resignation of Brian Little earlier in the month.