Toffees boss David Moyes watched the defender from the stands in Molde’s Europa League tie on Thursday, but Solskjaer is prepared to fight to keep hold of his player.
“We have in mind that they [Everton] may bid for Vegard,” Solskjaer told Nettavisen.
“There are many who have been and seen him many times. We’ll see later if anyone really wants him that they are bidding. But cheap he is not.”
The player himself however feels that he is ready for a move to the Premier League and appears willing to talk to the Merseyside club.
“I can not stand here and say that I’m not interested,” said Forren.
“After all the Premier League is involved, and Everton are a great club. But right now my focus is on performing well.
“I feel ready. I have had many great matches in the Europa League in the league and the national team.
“I have done well and it tempts me more and more to take the next step. I have developed myself a lot this year.”