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.
It is understood 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.
"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.
"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," he added in Tuesday's press conference to preview Wednesday's league encounter with Chelsea.
"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."
Chelsea have already been active in the transfer market this month and Adkins is backing Rafael Benitez's side to be in the title picture come the end of the season, even though the Spaniard has had a rough ride from supporters since taking charge of the European champions.
"I think with the addition of Demba Ba now and whoever else they might bring in they look a very well-equipped side to go for the title," he said.
"It will be an interesting one but obviously he (Benitez) has started well in respect that they have won games, he is a good manager and has won the European Cup and the team play good.
"They have got exceptionally good football players who play good football and if you give them half an opportunity they will capitalise on that."
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.