He told BBC Radio Kent: "I'm always going to be linked, but I won't be putting my application in.
"I'm ambitious and if a job came at the right club my chairman won't stand in my way."
Hessenthaler's spell as manager at Priestfield ended six years ago with the club in the Championship and he remained as a player for a further year.
His Dover side only missed out on a third promotion in a row when they were beaten in the Blue Square South play-off semi final to Woking.
He added: "Fans are not silly, players and managers are ambitious. I'm an ambitious man like everyone else. My chairman knows that.
"But I am focused on Dover. We have a big summer ahead of us."
It's a very attractive job at a club that is ambitious and has massive potential
Gillingham chairman, Paul Scally
Gillingham chairman Paul Scally said there has been no contact with Hessenthaler about the vacancy.
He said: "Not in so far as the manager's role, no. I had a text from him as a friend when we got relegated but I got a text from lots of people.
"I will no doubt catch up with Hessy for a beer at some stage and we will talk about what happened, but I have no more thoughts on that as far as management is concerned.
Stimson left his role as Gillingham manager by mutual consent on Monday morning after the club were relegated for the second time in three seasons following their 3-0 defeat to Wycombe.
Scally will today meet assistant manager Scott Barrett and coach Mark Robson to discuss their futures, and will make the decision on the retained list.
He said: "I've had 20 to 30 applications already. It's a very attractive job at a club that is ambitious and has massive potential, but I can't think about new managers until I sort out the issues I have to sort out.
"The retained list has to be in by Saturday and that is something I will do with the club secretary, and take a stab as to who is on it and who is not. I suppose I am the temporary manager so I will have to make that call."
Source: BBC Sport
Source: BBC Sport