Spurs have chased the Denmark international heavily over the past few months. Indeed reports claimed he is boss Jose Mourinho’s top target this summer.
Everton were also keen but, according to the Daily Mail, Tottenham have made a crucial breakthrough.
Talks have further advanced and the newspaper now claims Spurs will strike a £15million deal “this week”.
Hojbjerg looked likely to leave after announcing his lofty career ambitions to become a Champions League winner. After that, he refused a new contract and manager Ralph Hasenhuttl stripped him of the captaincy.
The 25-year-old has entered the final year of his deal, meaning Southampton have had to bring their valuation down. The Saints initially wanted as much as £35million, but the financial impact of the pandemic has also forced the price south.
Everton had reportedly agreed terms but Hojbjerg has held out for his favoured club, the Daily Mail adds.
Alongside the deal for Hojbjerg, Tottenham full-back Kyle Walker-Peters will go the other way, the source claims.
The England Under-21 international impressed with the Saints in his half-season loan agreed in January and the south coast club are close to signing him for £12million.
Last month, Mourinho admitted that he would not say no to Walker-Peters securing a permanent move away.
He said: “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 be playing every time and leaving 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.”