Dutch duo Van Gaal and Koeman are believed to have been City targets
Three of the leading contenders for the Manchester City manager's job have ruled themselves out of the running.
BBC Sport understands the club is keen to appoint a continental coach and Louis Van Gaal, Ronald Koeman and Gerard Houllier were in the frame.
But Koeman's agent told BBC Sport: "Ronald has one more year with PSV and would like to fulfil the contract."
Spokesmen for Houllier's Lyon and Van Gaal's AZ Alkmaar said the duo would not consider moving to City.
Erik van Leeuwen, the press officer for Dutch side AZ, told BBC Sport: "Louis has just renewed his contract at AZ and he will not go to Manchester City.
"Perhaps in the future he might consider one of the UK's top-flight teams but certainly not at the moment."
We have spoken with two Premier League clubs in the last three weeks, but not Manchester City
And Lyon denied rumours that Houllier could be moving to City or even Dynamo Kiev.
"We repeat that Gerard Houllier will next year be the coach of Lyon, with whom he is under contract until June 2008," a statement on the club's website read.
Meanwhile, Koeman's representative, Gerrit Lagendijk, said: "We have spoken with two Premier League clubs in the last three weeks but not Manchester City.
"Even if Manchester City is coming up at this time, we would have to say no."
City are on the look-out for their 19th manager since the departure of their legendary boss Joe Mercer in 1971.
Any move could hinge on the outcome of takeover talks with former Thai Prime Minister Thaksin Shinawatra but such a buy-out is thought to be close to fruition.
The bookmakers' favourite is former Chelsea boss Claudio Ranieri, who is in charge at Italian side Parma until the end of the season.
On Tuesday, Ranieri told BBC Sport he was keen to return to the Premiership but had not been contacted by Manchester City.
Stuart Pearce was axed less than 24 hours after the end to a disappointing season in which City finished only four points above the relegation zone.
Shinawatra's financial advisers are expected to complete their due diligence on the club this week and are then expected to indicate if they will proceed with a formal bid.
If a takeover fails to materialise, City chairman John Wardle has vowed to make funds available to strengthen the squad this summer.