Shane Long is on course to become the second most expensive signing in Saints’ history after Hull City accepted a £12.5m offer for the striker.
The 27-year-old Republic of Ireland forward will discuss personal terms before undergoing a medical at St Mary’s, with the club optimistic of tying up his signing quickly.
Only Dani Osvaldo has cost the club more, with the Italian requiring an initial £12.9m to bring him in from Roma last summer.
Saints boss Ronald Koeman is hoping that the captures of Long and centre half Florin Gardos, who is also expected to join this week, will leave Saints ready for the new season, which kicks-off at Liverpool on Sunday.
Saints had considered a move for Long in January, after the striker was identified by the club’s scouting and recruitment department as a somebody who would fit neatly into the team. A move has been swiftly made now after Koeman asked for another forward to be signed.
The potential size of the reported fee would surprise many people, though, especially as Long has never reached double figures in a single Premier League season.
However, with the new campaign about to get underway, Saints are keen for a quick resolution to any deal and would know that Hull would likely want a significant profit on the £6m they paid for Long in January in order to sell so quickly.
With plenty of ammunition in the transfer budget as well, following a summer that has featured some big-money departures, the club can undoubtedly afford to pay a premium.
Long, who has 47 caps and 11 goals for the Republic of Ireland, has only been at Hull since January, when he moved to the club from West Brom.
In his short spell with the Tigers, he made 15 Premier League appearances and scored four times.
Prior to that, Long had been at West Brom since August 2011, after signing from Reading for £6.5m.
He netted 19 top-flight goals in 60 starts and 21 substitute appearances for the Baggies.
Long had previously enjoyed six good years with the Royals, who picked him up from Cork City, scoring 54 times in 203 appearances across all competitions.