Saints remain hopeful of agreeing a fee with Feyenoord for striker Graziano Pelle, after increasing their offer for the player.
As revealed by the Daily Echo on Monday, the club are in negotiations for the Italian forward, as well as for FC Twente midfielder Dusan Tadic.
Saints are understood to have initially tested the waters with an offer of just over £3m for Pelle, who new manager Ronald Koeman wants to sign from his previous club.
That was rebuffed, as it fell well short of the Dutch side’s valuation.
Earlier this week, Saints went back in with a more serious bid, of about £6.4m (€8m), which is far closer to being an acceptable sum.
An agreement has still not been reached between the clubs, but it is believed they are not too far away from a suitable settlement now.
A deal for Tadic looks likely, with Saints believed to be keen to wrap up the transfer in the coming days, although there is also interest in the player from Schalke and Sevilla.
The Serbian playmaker, who was still training with Twente yesterday, is seen as the ideal replacement for Adam Lallana, who completed his move to Liverpool earlier this week.
Tadic, 25, was the fourth top scorer in last season’s Eredivisie, while he also contributed the most assists of any player in the Netherlands’ top division.
Pelle has been the standout striker in the same league for the past two seasons.
The 6ft 4in forward, who turns 29 within the next two weeks, has netted 50 goals in 57 appearances for Feyenoord in the Eredivisie since the start of the 2012/13 season.