Koeman, now Southampton manager, worked under Van Gaal at Barcelona but the pair fell out when they were at Ajax in 2004, when Koeman was coach and Van Gaal the technical director.
They shake hands on meeting now, according to Koeman, but Van Gaal referred to his former protege as "weak" in his autobiography and the closeness they once had never returned.
Van Gaal described Koeman as "a very good coach" but refused to talk about their relationship since the falling-out.
The United manager told a news conference at the club's Carrington training centre: "I don't have to describe my relationship with the trainer of the opponent..
that's more private.
"We play against Southampton and we have to speak about Southampton not speak about the coach."
Koeman took a similar line, saying: "The game is Southampton v Manchester Untied and the game needs that attention and not the attention about both managers because that's private.
"That was a working problem and I have to explain like that.
"It's not an issue because it is eight or nine years ago and now I prefer to talk about the game."
Asked about the relationship now, Koeman added: "Good
If we see each other we shake hands and that's enough.
"He's a great coach
He needs time, he will get the time of the club.
"It was difficult at the start of the season for them but I think they are on the way back and that showed the performances of the team and they won the last four games.
"It's a nice challenge for us on Monday."
United can go third if they beat Southampton, who are a point ahead of them in the table, and then face Liverpool but Van Gaal disputed suggestions the match against their Merseyside rivals was more important.
He also believes the Saints can still be in the Champions League places at the end of the season.
Van Gaal said: "Southampton play better at this time and have more points at this moment than Liverpool so I think it's good that we have to play Southampton now.
"I think they have a good squad, a lot of players that I know and who were offered to us
I think they are able to come in the top four but that's also because I believe in the management in Ronald Koeman and his brother [Erwin]."
Van Gaal also responded angrily to reports that he will be handed Â£100million or more to bring in new players.
He added: "I think it's disgusting always writing about numbers
I don't think that [United executive vice-chairman] Ed Woodward said anything about that, I don't think I have said anything about that.
"It is disrespectful to my players and I don't like to talk about it
I have to work with the selection I have and I have respect for my selection and I believe in my players."
Wayne Rooney will be fit to face Southampton, Van Gaal confirmed
The United skipper had a scan on Thursday to examine a possible knee problem but has been given the all-clear.
However record signing Angel di Maria will not be ready to return from his injury in time for the trip to the south coast.
Jack Cork is Saints' latest casualty with an ankle injury.
Source : PA