Norwegian forward Tessem has been told he can leave St Mary's and he is currently in the process of tying up the loose ends before finalising his exit from The Saints.
Tessem spent a portion of last season on loan at Lyn and they have struck a deal to sign the forward if he opts to return to his homeland.
However, another European club could step in and Aalborg have expressed an interest.
"I have no comment to make regarding Aalborg," Tessem told VG.
"First of all I need to sort out my contract with Southampton, before I can start to think about extending my career."
Lyn are aware they could be beaten to the punch to the signature of Tessem, as director Morgan Andersen said: "We have got a deal with Jo and he will join us if he comes back to Norway.
"But there is every chance that he can sign for a foreign club."
