But, according to Football Insider, the figure could be slashed by a fifth to £20m in order to move him on.
Hojbjerg was stripped off the captain's armband before the Premier League restart due to his reluctance to sign a contract extension.
Southampton boss Ralph Hasenhuttl said: "No, he will not be captain.
"We had an agreement, and [I] made clear that if you decide not to extend your contract, you will not be captain of this team.
"He knows that he is an important player for this club. I think we have found a good agreement."
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Tottenham are unlikely to spend big in the window after taking out a £175m Bank of England loan, which has not been earmarked for transfers, to steer their finances through the coronavirus crisis.
Spurs could resort to a swap deal if they are unwilling to spend £20m on Hojbjerg.
Kyle Walker-Peters is on loan at Southampton and could potentially be swapped.
While Walker-Peters is highly rated by the club, Mourinho has indicated he would not stand in the player's way if he wishes to depart on a permanent basis.
Tottenham could sign Pierre-Emile Hojbjerg for £20m (Image: GETTY)
"He's a kid everyone loves here, Daniel Levy himself has special care for the player and he's here for years and years and years," the Tottenham boss said.
"So we let him go because we think he has the right to be happy. He's happy now I think. Playing and playing well.
"I'm not in control of the transfer decisions but the general feeling is there's a place for him here. But if his desire is to leave the club in search of happiness I don't think we'd stop him.
"He's a player with a good value in the market but I don't think we'd stop him doing it."
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