If he refuses and an offer comes in then it will have to be seriously considered as his value diminishes over the next 12 months.
"We don't want Joe to go, we want him to sign an extension," said Jones.
"We haven't started silly week of the transfer window. Everyone's seeing what is around and what they can get before letting people go, we're no different.
"There've been no enquiries for Joe at the moment," Jones told BBC Sport Wales.
"We get a lot of whispers, but we want him to stay and hope no-one else comes in for him.
"Joe's a good professional, he'll just get his head down and work hard."
As fans we know that City, like most other clubs, are a selling club. It would be good though to see Joe sign a new deal like Ross McCormack and the newly re-signed Michael Chopra.
I appreciate these lads have Premier League ambitions. Maybe they could get that with Cardiff.
Jones is looking to add to his squad and doesn't want to lose anyone else. He would like three more players to come in.
"I keep pestering and chipping away at the chairman. I know what players I want, I've told him.
"If I can get the three I want it will strengthen us even more and that's what we're all looking for.
"There's no sign of anyone else going, we've had one or two enquiries but it's early days yet.
"We have to be careful. We can't let everyone go, we have to stay strong."