Hendon has left the club to take up the role of development team coach at West Ham
Hendon, 39, joined Hessenthaler's coaching team last summer following a brief spell as manager of non-league Dover but has spent just one season at Priestfield.
The Gills boss would prefer to bring in a new coach rather than a number two and hopes to be able to make an appointment next week.
He told the club's official website: "There is a void there and I am certainly looking at bringing somebody in so I'll be sitting down with the chairman to see which way we go with that."
Hessenthaler added: "Ian has gone now. The situation was that (Hammers first-team coach) Wally Downes, who worked with us last year, made a call to me and asked if they could offer him the job.
"I didn't want to lose Ian but, as a friend, I had to ask him the question. He wanted to speak to them and they offered him the job, so I couldn't stand in his way. I think the chairman is looking into the situation at the moment but Ian has gone."
Meanwhile, Gills are anxiously awaiting news on new signing Adam Birchall after he left the field during Tuesday night's 3-0 friendly victory over Welling on a stretcher nursing a knee injury.