Saints are edging closer to securing Feyenoord striker Graziano Pelle and FC Twente midfielder Dusan Tadic.
The club are attempting to make the pair the first signings of the Ronald Koeman era at St Mary’s and are hoping to now seal both deals next week.
As reported in Monday’s Daily Echo, Saints have been in negotiations with Feyenoord and Twente for the players, with progress having been made on both fronts this week.
They are understood to have raised their initial bid for Pelle to about £6.4m (€8m) and an agreement with Feyenoord is believed to be close now.
Their move for Serbian playmaker Tadic, who is viewed as an ideal replacement for Adam Lallana and is likely to cost around £9m, is also progressing.
Sevilla, who are also interested in the player, are said to have declared defeat in the race as they cannot match Saints’ financial power.
There is a growing confidence on both deals and Saints hope to finalise them next week, ahead of Koeman conducting his first media duties on Friday.
Ideally, they would like them to be done in the early part of the week.
Both players would arrive at St Mary’s after shining in the Dutch top-flight.
Pelle bagged a total of 50 goals in 57 appearances over the past two campaigns, after being brought to Feyenoord by Koeman.
The 6ft 4in forward, who turns 29 later this month, is keen to follow his old boss to the Premier League and try to prove himself in England.
Tadic, 25, is also extremely highly-regarded in the Eredivisie.
He enjoyed an outstanding season with Twente last term, scoring 16 goals from midfield and helping the team to a third-place finish.
He also provided 14 assists and created an eye-catching total of 133 chances – in both categories, he led the way by some considerable distance.
Tadic, who made his international debut at 19, has been capped 25 times by his country.
He has also attracted interest from Schalke, but Saints look favourites to land him.