Hill, the 1996 world champion in Formula One, begins his second season with Jordan-Mugen in Australia, a week on Sunday, on a high after delivering the team's maiden victory six months ago.
Jordan will offer Hill a new contract if he sustains his form this year but recognises that the Englishman, at the age of 38, will not wish to prolong his career should he no longer figure as a championship contender.
"How long Damon can go on I don't know," Jordan said. "If he does a good job for us we'll want him to stay. If he doesn't, he'll want to stop himself. He'll be strong enough to make that decision.
"If things are getting too tough for him and on top of him he would be the first to come to us and say "I'll go at the end of the year'. There would be no drama, he would leave with dignity. The last thing anyone wants to see is a world champion falling below his standards.
"If he did stop driving he could even stay on with us as a consultant. He feels committed to this team and we are to him. No one will take away from him the fact that he was the first driver to win a grand prix for Jordan."
Hill won the championship and 21 races with Williams, but Jordan believes he will treasure above all others his 22nd, earned ahead of his then team- mate, Ralf Schumacher, in last season's Belgian Grand Prix.
"Damon will think that was the sweetest of them all because it was so unexpected. I'm sure that's the one he'll tell his grandchildren about."
Hill's new partner is another German, Heinz-Harald Frentzen, ironically the man who replaced him at Williams, but Jordan is confident the pairing will enhance the team's prospects of improving upon last season's fourth place in the constructors' championship.
"We're getting better vibes from Damon than we did at the start of last season," Jordan said. "The car's better and he knows that. He knows the company better. He comes in to see us and he's understanding the team more. He's seen the development of the car and he's very positive about it. He's also positive about Frentzen.
"In race circumstances Damon's still strong. When you give him the car and the oomph, he'll deliver all right. He's a very clever, foxy individual. Some call into question his commitment, but having worked with him for a year I can see his commitment is beyond reproach.
"It would have been easy for him to give up after Williams but he put himself out on a limb and stuck at it. He had a difficult year with Arrows and a difficult start with Jordan, with people saying don't go on. But he did go on and proved a lot of people wrong.
"He and Heinz-Harald are getting on well and although they will race each other they are experienced enough to put the team first.
"We are desperate to finish in the top three of the championship and expect our drivers to do everything possible to achieve that."Reuse content