The Denmark international was at the club's Hotspur Way training complex to undergo health checks, the PA news agency understands.
Hojbjerg is primed to join Spurs for a reported initial £15million, which could rise to £19m, with right-back Kyle Walker-Peters set to go the other way in a separate deal.
Hojbjerg has been intent on joining Spurs, liking several social media posts linking him with the club and the deal could be completed in the next 48 hours.
Walker-Peters' move is a separate transaction as Saints look to make his loan into a permanent transfer – a deal which is still being finalised.
The right-back spent the second half of last season on loan with Ralph Hasenhuttl's men and impressed, prompting Southampton to pay a reported £12million for his services.