The Chelsea left-back made a huge impression on the Robins during his loan spell this season
Bristol City do have an option to buy the player due to the terms of his loan deal, and Johnson confirmed City have spoken with the 21-year-old.
"We're in constant discussions with Jay and his agent and we're quite relaxed on it because you can't force a player to do something that he doesn't want to do," said Johnson on BBC Radio Bristol (via Bristol Live).
"And it's not that he doesn't want to do it, it's just that it's got to be right.
"For a player like Jay to commit to Bristol City is something that I believe would be the right move for him. But at the same time it's got to be right for all parties.
"We're all ambitious and Jay's ambitious as well as a football player and hopefully the club will fulfil that ambition and he'll end up at Bristol City."