Saints have had a £7m bid for Jay Rodriguez accepted by Burnley.
As revealed last week, the two clubs were in discussions regarding a deal worth in excess of £6m for the striker.
The Clarets, who are resigned to losing the 22-year-old this summer, had valued the player at £8m.
But with the forward having just one year left on his Turf Moor contract, the Championship side have been willing to accept a smaller sum.
If Rodriguez does move to Saints, the fee would break the club's long-standing transfer record, set when they signed Rory Delap for £4m from Derby in 2001.