McGhee has signed former Norwich goalkeeper Stuart Nelson on a one-year contract after back-up Bertrand Bossu suffered an injury.
But a move for Johnson is in doubt after the 21-year-old Amiens defender reportedly turned out for Plymouth in a friendly against Morecambe.
McGhee travelled to Paris on Thursday for talks with Amiens and the player's agent and declared himself close to the signing on Saturday.
However, Argyle boss Paul Sturrock may beat McGhee to the deal.
"We're still trying for Reda Johnson but we're in danger of being gazumped," McGhee said.
"It's dragged on a little bit and there is talk we've heard he is talking to other people which is understandable - he's a good player.
"When people ask about trialists' names and it comes out public there is always a danger that they get invitations from other clubs. We're still hopeful but not certain."
McGhee moved quickly to wrap up a deal for Nelson, who was released by Norwich this summer.
Nelson did not play for Norwich during his one season with the Canaries, who are managed by McGhee's former Dons team-mate Bryan Gunn.
The 27-year-old - who will provide cover for Jamie Langfield - was previously a regular with Leyton Orient and Brentford.
Nelson will start on the bench in Thursday's Europa League qualifier against Sigma Olomouc after the injury to Bossu left Aberdeen without experienced cover for Jamie Langfield.
"We have a problem with Bert," McGhee said. "He looks like being out for four or five weeks. I wasn't prepared to go into the European games without cover.
"We couldn't find anyone in the really short term who was good enough so we went for a lad for a year who we know is capable of going in for either of these games.
"We're confident we've got a goalkeeper who can put pressure on Jamie for his position and also provide cover."
Nelson told www.afc.co.uk: "I am delighted to have signed for a club of the size and stature of Aberdeen.
"My agent received a call from Mark McGhee at the end of last week and it's great to have sorted out a contract so quickly.
"I'm already looking forward to meeting my new team-mates and can't wait to see the club in European action this week."