Belgium international Alderweireld has been linked with several Premier League clubs this summer, with Arsenal, Newcastle United and West Ham United reported to have shown an interest.
However, Alderweireld is now holding talks over a season-long loan move to St Mary's as Koeman tries to complete two signings on the final day of the summer transfer window.
"I am still looking to bring in two more players, an attacker and a defender," Koeman told Dutch website Helden Online.
"Toby Alderweireld will undergo a medical today. Hopefully we can also add another attacker. I can't say who we are working on."
Koeman also confirmed that he has not considered a move to sign Ajax goalkeeper Kenneth Vermeer, who is expected to join Feyenoord.
He added: "We didn’t think about Kenneth Vermeer. We have bought Fraser Forster, who is 26 years old and a fantastic goalkeeper, who is part of the England squad."
The Dutchman also acknowledged that deals for Aston Villa defender Ron Vlaar and Dynamo Kiev forward Jeremain Lens ‘didn’t succeed’, and that he opted against an approach for Queens Park Rangers new boy Leroy Fer due to the number of midfielders already at his disposal.
Meanwhile, Koeman has discussed the early impact of summer signing Graziano Pelle, who scored his first Premier League goal in Saturday's 3-1 at West Ham.
"Pelle still has to adapt," said Koeman. "In the Netherlands, he won 80 per cent of the battles, even if at times he was too late. Here, he will win 50 per cent at most.
"Graziano has to become sharper, but we will give him time. If he scores 10 to 15 goals, he has done well. For us, he has been important already."