Entering the final year of his contract, the Danish international has made over 100 appearances for the Saints since his arrival from Bayern Munich in 2016.
However, his future looks destined to be elsewhere with Everton and Tottenham Hotspur both showing interest after the midfielder was stripped of the captaincy having announced his desire to leave the club.
“I know what I want,” said Hojbjerg, speaking to Sport1 in May. “The club knows it too. I want to play at an even higher level than I am currently.
“The relationship between me and Southampton is fantastic. The club gave me the platform to grow. I am not saying ‘goodbye’ and I am focused on my club, but my goal is very clear: I want to win the Premier League and the Champions League.”
Search for a replacement
One replacement could be the return of Adam Lallana, whose contract at Liverpool expires at the end of the current campaign.
Lallana, now 32, left Southampton for Anfield in July 2014 in a £25 million deal, and his old club will be keen to have him back to fill the gap Hojbjerg would leave.
Saints though will be bound to face competition of his signature, with Lallana’s former boss Brendan Rodgers said to be interested in bringing him to Leicester City whilst Brighton and Burnley have also expressed interest in the former England international.
Lallana rose to prominence at Southampton after graduating from the club’s famed youth academy.
The St. Albans-born ace was a prominent member of the Saints squad that bounced back from the lows of League One to record an eighth-place finish in the 2013/14 Premier League.
A busy window?
It looks set to be a busy summer at St. Mary’s, with Saints boss Ralph Hasenhuttl reportedly hoping to make Kyle Walker-Peters’ loan move from Tottenham permanent, whilst also being close to completing the signing of Real Valladolid centre-back Mohammed Salisu.
The Saints also looking at offloading other players with Wesley Hoedt, Fraser Forster, Mario Lemina and Guido Carilla all set to be made available in the clear out.