The Norway defender has impressed for both club and country in 2012 and reports have suggested he could soon be heading to the Premier League.
Everton manager David Moyes has been to watch him in action, while Manchester United and Fulham have also been linked with the 24-year-old.
However, Solskjaer has warned that Molde are under no pressure to sell and will demand a good price for the centre-back.
"We haven't received any offer for Vegard." Solskjaer told Romsdals Budstikke.
"But there are many who have enquired about Vegard. I am expecting that we might receive an offer in January.
"Either we get good offers for Vegard when the transfer window opens or we will be happy to keep him in Molde.
"We are not depending on player sales for financial reasons."
Solskjaer also confirmed that Molde had rebuffed an offer for one of the other players at the club.
He said: "We have received one offer from a foreign club for one of our players, but it is not interesting for either the player or MFK."
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