The Scotland international has made just four Premier League appearances in 2014-15 and Sam Allardyce has been keen to push through a move for the midfielder.
Fletcher is at West Ham for talks as he seeks regular playing time, with Van Gaal sad to see the 30-year-old go.
"He is at West Ham now I believe, so we will have to wait and see," Van Gaal told reporters
"He is my third captain so he is an important guy in the dressing room, I like him as a person so we shall miss him.
"He hasn't played many times and that's always the main goal of a player. We spoke about it and he prefers to play."
Hammers manager Allardyce was optimistic of sealing the signing on Thursday, with West Brom boss Tony Pulis also confirming his interest in Fletcher.
has been a loyal servant for us and i wish him all the best in his new club....MANCHESTER UNITED ALL THE WAY
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