The 27-year-old defender has an option to extend his contract for a second season but is yet to commit to the Sky Blues.
Mowbray is keen to keep Johnson, despite him only playing 20 times last season following several injury problems, and is trying to convince the player.
“Without saying it’s a done deal or anything like that, I’m hopeful,” Mowbray told the Coventry Telegraph.
“I would say it’s ongoing. I have spoken to Reda’s agent half-a-dozen times over the last few weeks, even on my holidays. I get on well with him and have known him a lot of years. I’m hopeful with that but he’s also potentially got other offers coming his way.
“There’s still a lot of talking to be done and as I have told Reda and his agent I would like to keep him at the football club and have a real positive push to get out of this division.
“None of us want to be in this division. We want to at least be in the next one with a chance of getting into the Premier League. We all understand that and hopefully we can give Reda a platform to achieve his ambitions.”