The 23-year-old midfielder is rated at around £2m but Celtic, who beat Trabzonspor 3-1 in their first match in the Antalya Cup last night, will face competition from a number of European sides.
"Celtic are one of the clubs showing interest in Stefan," said Jostein Flo, Stromsgodset's sporting director. "But there has not been anything more than that, just now." Tore Pedersen, Johansen's agent, added: "There is nothing concrete, but I can confirm there are many European clubs interested."
Ronny Delia, the Stromsgodset manager, expects Norway's player of the year to move on despite the offer of a new contract.
"I wouldn't completely rule out him signing a new contract - nothing is impossible in football," said Delia. He is sensible and we are a reasonable club. It depends on what offers he gets. We'll see what happens."
John Carew, the former Norwegian internationalist, has recommended Johansen to his former club Aston Villa. "Villa should definitely take a closer look at midfielder Stefan Johansen," he said. "He would be a good addition to the team. He's player of the year back home, young, has the heart of a lion and has the stamina of a Duracell rabbit. He's also humble and hard-working. I've been asked by Villa fans about who they should sign this month and I told them they should go for Stefan."
Celtic have also been linked with a move for Stephen Kingsley. The Falkirk full-back is thought to have caught the eye of the chief scout John Park but, as with Johansen, Celtic are not the only club interested in the 19 year-old.
"Clubs from Scotland and England are looking at Stephen," said Falkirk's technical director Alex Smith. "There is a lot heavy of interest in him which is understandable. Stephen is a typical modern-day attacking left-back. He is a very good defender who gets forward as well. He is two-footed but has a very educated left foot and he is also exceptional at left centre-back.
"When you look at him Stephen has got to be one of the best left-backs in Scotland and he is getting better all the time."
One player likely to be leaving Celtic, at least in the short term, is Tom Rogic. The Australian has failed to establish himself in the first team and could be allowed to leave on loan until the end of the season, with the player needing regular football ahead of this summer's World Cup finals. Japanese club Vegalta Sendai, managed by the Australian Graham Arnold, are understood to be interested, and Lennon is said to be sympathetic to Rogic's needs.
Ange Postecoglou, manager of the Australian national team, plans on speaking to the Celtic manager to ensure Rogic is match fit ahead of the World Cup.
"I'll get my message across to Neil Lennon, yeah," he said. "I'm hoping over the coming weeks that a decision is made. Tom is at a fantastic football club but the reality of it is in a World Cup year he needs to be playing so if that means going somewhere else, as a national team manager I'd be much happier with that. I really need players playing and fit around selection time so there's some pretty big decisions to come up."