The former Manchester United striker, who is currently in charge of Norwegian champions Molde, has been repeatedly linked with the job at the Reebok Stadium following Owen Coyle's dismissal last week.
However, the 39-year-old says he has no plans to leave Molde before the end of the season, although there is just over a month to go.
"There will always be speculation when someone in England needs a new manager," he told Norwegian newspaper Romsdals Budstikke.
"There are surely 20 names who have been linked with Bolton now and it's natural that mine is among them. But it's not for me.
"Blackburn, Bolton, rumours crop up all the time. But I'm not that bothered about them.
"I'm absolutely certain I will see out the season here (with Molde), I can promise that."
Solskjaer had already turned down an approach from Aston Villa earlier this year after holding talks with the midlands club, while he has also been named as a potential successor to Steve Kean at Blackburn.