Solskjaer left the Norwegian outfit to take over at Old Trafford until the end of the season following Jose Mourinho’s dismissal in December.
But Solskjaer has since won all seven of his matches in charge of Manchester United and brought the feel-good factor back to the club.
Mauricio Pochettino and Zinedine Zidane are still being considered for the role.
But Molde star Alex Craninx has discussed Solskjaer’s future – and it appears players and staff at the Norwegian club believe their former manager won’t be returning in the summer.
“But, honestly, I don’t think he’ll return”
“When his technical staff left, he stayed in touch and he sent us a message saying that we prepared well during the pre-season, that we would see each other when his transfer to United was over,” he told Marca.
“But, honestly, I don’t think he’ll return, he should continue for how he is doing it.
“It’s not easy to manage in the Premier League and win the first seven matches [he has 19 goals in favour and only four against.
“He knows the club, was important as a player and is doing well.
“Things have changed a complicated dynamic, if they finish in the top four, I do not think they want to get rid of him.”
United fans certainly think Solskjaer should be given the role on a full-time basis.
And club legend Gary Neville has championed his former team-mate to continue in the job.
“Ole has done an incredible job at Manchester United over the last six weeks – far better than I could have imagined,” he told Sky Sports.
“Tottenham was a huge game and are a huge team who we’ve all loved watching.
“But in that first half, he changed to a diamond and changed the shape.
“He was bold and took risks and it paid off – that’s what Manchester United is about and he’s delivered brilliantly.”