The Norway international had reportedly been set for a trial with Liverpool this week, but the south coast club are believed to have lodged a bid for his services.
And, whilst Adkins remained coy when asked whether or not the 24-year-old is close to a move to St Mary's, the Saints boss did not rule out the move.
Adkins told reporters: "From our point of view, like everything, through the transfer window there's always going to be speculation, there's always going to be people talking about different deals.
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"There's already through this transfer window and in January, there have been one or two cases where a player is meant to be at one club, the next minute they've gone and signed for another football club.
"The speculation's there, this is obviously the latest one that we've talked about. When things happen, if they happen, then our football club will announce it."
Despite his unwillingness to reveal whether the club are close to completing a deal, the 47-year-old did express his admiration for the defender.
He added "I know he's a Norwegian international. He's left-footed predominantly, he's got a lot of games under his belt for a 24-year-old player. As I say, he's got a bright future in the game."