Southampton have released a statement claiming that they want a new manager that can "take the club to the next level".
The Saints confirmed on Tuesday morning that they have accepted the resignation of Ronald Koeman, who has gone on to take charge at Everton.
The Dutchman was in charge of Southampton for two seasons and took them to sixth place in the 2015-16 Premier League campaign.
Now, the coastal club are searching for a replacement who will share the outfit's "values and ambitions".
A statement on their official website read: "Southampton Football Club can today confirm it has accepted the resignation of first-team manager Ronald Koeman, and completed negotiations with Everton over his move to Goodison Park.
"The search has already begun for the right appointment who can take the club to the next level and build on our track record of recent success, which culminated in a sixth-place finish in last season's Premier League, as well as qualification for the group stages of the Europa League.
"Our focus now is to build on our long-term plan, and work with a new management team who share both the club's and our supporters' values and ambitions."
Frank de Boer and Eddie Howe have been named as possible targets for the Saints.
