The 24-year-old centre-half is expected to meet with the South Coast club to discuss a possible deal, with Everton and Reading also interested in the defender.
Liverpool manager Brendan Rodgers was recently reported to have invited Forren for a trial at the Merseyside outfit, but Solskjaer confirmed that only the Saints have made a bid.
“There have been many inquiries from various English clubs, but Southampton submitted an offer,” Solskjaer told Norwegian newspaper Romsdals Budstikke.
“It was very interesting for us and Vegard. We are more or less agreed with the club, but nothing is 100 per cent confirmed.
“Molde is close to a deal, so we’ll see if this is something that all parties will go with.”
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news