The 28-year-old, who has been valued at £10m by club majority shareholder Steve Lansdown, was named on the bench for the Robins' Championship opener against Barnsley on Saturday.
"The owner has come out and said what he will accept," Johnson told Sky Sports News. "I am not convinced Birmingham have the money to do that, but it's important we leave the door open for Aden.
"We haven't fallen out. You saw the reception he got from the fans, everybody loves him here.
"We just move on whether he stays or goes, but that's the problem sometimes with the window. If it shut tomorrow I would be absolutely delighted."
Flint featured in each of City's 46 Championship outings last season, scoring five times.