Monday evening will see a fascinating clash between apprentice and master at St Mary's, where Holland great Koeman takes on the man he spent time coaching under at Barcelona.
However, their relationship took a downward turn 10 years ago when the pair worked together at Ajax, with manager Koeman feeling undermined by technical director Van Gaal.
The United boss referred to him as "that boy" in his autobiography, also describing his former protege as "weak", but the frosty relations appear to have thawed in recent years.
That said, neither were keen to talk about their relationship in the build-up to Monday's game, although Koeman interestingly backtracked on his initial insistence that things were now "good".
"I don't say good, it's correct - maybe that's the best word," he said.
"When he was the national coach and I was the coach of Feyenoord, we had contact about the international players, but there are too many questions about him."
The pair spoke regularly in the build-up to the World Cup, with Koeman's Feyenoord side providing five players Van Gaal took to Brazil.
Furthermore, the United boss also asked how best to implement the three-man central defensive system not only subsequently used by the Oranje, but United as well.
Both sides are likely to revert to an orthodox four-man defence on Monday, but Koeman expects them to approach the game with a similar philosophy.
"We are both Dutch managers, we like to play offensively, we like to dominate the game, but for different reasons," he said
"It's not my job (to control how United play)
Manchested United play a different system.
"In the last few games they played 4-4-2 with a diamond in midfield and maybe they will change for Monday, we will see.
"Still the manager likes to play attractive football, to score goals and create.
"Sometimes for lots of reasons you can't do that, but that's not my problem."
What is of concern to Koeman, though, is Saints' injury-hit midfield.
Morgan Schneiderlin, Jack Cork and James Ward-Prowse are absent for the visit of United - even defender-cum-midfielder Toby Alderweireld is a doubt.
It could mean a first Premier League start for 19-year-old Harrison Reed, alongside Steven Davis and Victor Wanyama.
The latter had an on-off first campaign following his Â£12.5million move from Celtic, but has kicked on impressively this term.
"He is an important player," Koeman said of the Kenyan.
"In the beginning he did it well and it was difficult for him because he had a different pre-season to the rest of the players because he had to play for the national team of Kenya, but little by little he is taking his place in the team.
"He's very strong
He wins his battles in midfield, he scores goals and that's the difference between now and last season.
"Morgan and him have a good relationship, they connect well in midfield, and Victor is maybe the most strongest, physical midfielder what we have in our team.
"He's doing well, he's a good professional and I'm happy to have him in our team."
Source : PA