Saints hope to seal the appointment of Ronald Koeman as their new manager early this week.
As revealed on the Daily Echo website over the weekend, the club submitted a formal contract offer to the 51-year-old on Friday night, having identified him as their preferred candidate to succeed Mauricio Pochettino.
Lawyers and advisers acting for Koeman spent the weekend going through the deal, and it is hoped an agreement will be reached shortly.
The Dutch legend returned from a holiday in Turkey on Sunday and began the process of putting his backroom team together.
Assuming he is appointed, Koeman is expected to hire his brother, Erwin, as his assistant, and the two are understood to have spoken further about the role in person yesterday.
Jan Kluitenberg, who was physical coach under the European Cup winner at Feyenoord, is also likely to come on board, but his former assistants Jean-Paul van Gastel and Giovanni van Bronckhorst are set to remain with the Dutch outfit.
Koeman first held talks with Saints two weeks ago, with the club impressed by what the former Netherlands captain had to say.
The ex-Barcelona player was also happy with the vision set out to him by the board.
Koeman was known for encouraging an attacking style of play at Feyenoord, with the club's fortunes improving dramatically during his three-year spell in charge.
He also brought through a number of young players at the Rotterdam outfit.
Saints have been wanting to appoint a manager with an attractive and attacking philosophy, while also being willing to promote talent from the academy, and they believe Koeman ticks those boxes.
During his managerial career, Koeman has managed a number of heavyweight clubs, enjoying great success with both Ajax and PSV Eindhoven.
Spells outside of Holland, with Benfica and Valencia, were far less triumphant, although he did reach the Champions League quarter-finals with the former and won the Copa del Rey with the latter.
His brother, Erwin, 52, has also previously coached Feyenoord, while he spent two years in charge of the Hungarian national team.
He most recently managed RKC Waalwijk, but left the club this summer.