Hessenthaler made the transition to his current role over the summer and Allen, the man who replaced him as manager at the Priestfield, has said he is continuing to play a major role in helping the club achieve their aim of promotion this season.
The Gills finished eighth in League Two last term, missing out on the play-offs by just two points.
Allen told Sky Sports: "Andy Hessenthaler has done a really good job over the last couple of years with the team.
"Andy has been very helpful and supportive of me, recruiting players and helping players settle in. Like an assistant manager almost.
Allen added: "The aim is to go up, let's be honest. The chairman is very ambitious."