According to Sky Sports, Spurs have offered £15m for the 24-year-old Denmark international in negotiations so far.
Saints are thought to value Hojbjerg at £25m, but a deal could be made for a smaller transfer fee and with on-loan Kyle Walker-Peters moving the other way to St Mary’s permanently.
Hojbjerg is set to leave the club in a bid to play regular European football. His contract at Southampton expires in 2021.
When does the summer transfer window open and close?
The summer transfer window opened yesterday on 27 July and closes at 23:00 on 5 October.
A domestic-only window for trades between Premier League and EFL clubs will run from 5 October until 16 October at 17:00.