Virgin wants to keep Glock
But with Renault, who has linked to ahead of this year's campaign, believed to be interested in signing the German, Virgin could face a tough task retaining Glock.
Wirth, though, is confident the former Toyota driver will remain at Virgin next season.
"We've got another year on the contract with Timo, but like anything in life everyone has got to want to carry on," Wirth told Autosport.
"Timo understood that we were a new team and he wanted to be part of something that was growing going forward. That's why the Silverstone weekend was so important because it has hopefully shown him that we can do it."
He added: "We were so lucky to have a driver with his talent, ability and experience join us at his age. It's up to us to try and deliver on that."
As for Glock's teammate, Lucas di Grassi, Wirth was full of praise for the rookie Brazilian.
"I know I'm very biased, but I think he is looking good for rookie of the year if you look at his relative performance.
"He's coming into his own and doing a fantastic job. The disadvantage is that Lucas is naturally a bit heavier than Timo. For all of the new teams, weight is an issue so he's still got a disadvantage. It's to do with us and we're working very hard on it."