The south-coast club have performed admirably over the past two years, after selling many of their star names.
The Dutchman only has one year left on the deal that he signed in June 2014.
The Mirror also claim that the Saints officials will present Koeman with a detailed blueprint of how they expect to achieve success over the next five seasons, including transfer plans, how their academy is run, and the general direction of the club.
The ex-Barcelona man has performed miracles at St Mary's. When he took the reigns from Mauricio Pochettino, many tipped the team from the south-coast for relegation, after a summer that saw many of their best players leave.
Adam Lallana, Dejan Lovren and Rickie Lambert were sold to Liverpool. Luke Shaw also left, heading north up the M1 to Old Trafford.
The mass exodus was complete when Calum Chambers was sold to Arsenal towards the end of the transfer window.
Koeman made a whole host of smart acquisitions however and guided Southampton to their highest ever finish in the Premier League, ending the campaign in seventh position.
Dusan Tadic, Graziano Pelle, Fraser Forster, Shane Long and Sadio Mane were signed for a combined £52 million. Further signings were made at the start of this summer, including the impressive capture of Ryan Bertrand from Chelsea.
Rumours have circulated of late about the former Dutch international's future, and Saints fans will be hoping they can tie their man down.
After a stuttering start, Southampton have recovered, and currently sit seventh in the table.