The 24-year-old centre-back has long been linked with a move to the Barclays Premier League, with Liverpool, Everton and Fulham believed to have shown an interest in acquiring his services.
Press Association Sport understands Molde have now accepted a bid from Southampton for the player, but Adkins said: "Like everything through the transfer window, there is always going to speculation and people talking about different deals and I think it is prudent that, until someone signs a bit of paper, you don't announce it."
He added: "Already in this transfer window in January there has been one or two cases where a player is meant to be at one club and then the next minute they have signed for another club. Speculation is there and obviously this is the latest one and when things happen, if they happen, our football club will announce it."
Molde boss Ole Gunnar Solskjaer contradicted Adkins claims earlier on Tuesday when he told Norweigian newspaper Romsdals Budstikke the club had accepted a bid for the player. "There have been many inquiries from various English clubs, but Southampton submitted an offer," he said.
Adkins did admit he had knowledge of Forren's ability, and in a press conference to preview Wednesday's league encounter with Chelsea, added: "I know he is a Norweigian international who is left-footed predominantly, he has got a lot of games under his belt for a 24-year-old player and he has got a bright future in the game.
"If something materialises for any player at our football club we will be the first to announce it."
The Saints were on the receiving end of a 5-1 thrashing when Chelsea visited the south coast in the third round of the FA Cup earlier this month, but Adkins does not feel that result will have any bearing on Wednesday's game.
He said: "It is a league game and that was an FA Cup game and for 40 minutes we did all right and kept the ball and then conceded, from our point of view, two goals too easily."
Adkins confirmed club captain Adam Lallana is back in light training but refused to give an expected comeback date. He also suggested Luke Shaw will be missing for the trip to Stamford Bridge after leaving the field on a stretcher with a gashed knee in Saturday's win over Aston Villa.
Source: PA
Source: PA