Manchester United have decided not to keep Radamel Falcao following the end of his season-long loan from Monaco.
The Colombian, who missed Sunday's 0-0 draw with Hull because of injury, scored just four goals in 29 matches.
United did not take up a reported £43.2m option to buy the 29-year-old, who failed to net in his last 13 games.
"Falcao is a top professional and a good human being. I would like to wish him well for the future," Van Gaal told the club's website.
The former Porto and Atletico Madrid striker's last goal came against Leicester on 31 January.
The South American, who missed the 2014 World Cup after suffering a serious knee injury in January last year, made a point of waving to the United fans when he was substituted in the 1-1 draw with Arsenal on 17 May, in what proved to be his last appearance.
It is the first decision in what is expected to be a busy summer for Van Gaal, who will look to reshape a squad he has consistently said is not balanced.
|River Plate (2004-09)||90||34|
|Atletico Madrid (2011-13)||86||68|
|Manchester United (2014-15)||29||4|
And while the 63-year-old is ready to go on an extended holiday to Portugal, after spending most of last summer guiding the Netherlands to third place at the World Cup, he intends to remain in touch with executive vice-chairman Ed Woodward.
"I am the manager," he said. "I have to decide which players are to go and which have to come. That is a process. It is not so easy. It is waiting for clubs to agree or not.
"It is hard work, but more for Ed Woodward than me. I go on holiday but I will always be in contact."
There was no update on the future of goalkeeper David de Gea, who missed the Hull game after failing to recover from a hamstring injury.
"He has to say something, not I," said Van Gaal when asked about the Spaniard.