Everton are thought to be leading the chase for Forren and Toffees boss David Moyes and his assistant Steve Round watched the centre-back in action on Thursday night in the Europa League clash with FC Copenhagen.
It is the second time in a month that Moyes has cast an eye over Forren after taking in Norway's clash with Hungary in Budapest.
Forren has enjoyed a fine season for club and country, helping Molde retain the Norwegian championship and a number of clubs have been linked with a move for the 24-year-old.
Solskjaer is aware of the growing interest in Forren from Everton, but insists there have been no bids as yet for the 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."
Forren admits he would be interested in a move to Everton and he feels he is ready to take the next step in his career.
"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."
He added: "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."