The Dutch tactician took to his Twitter page to bid the 34-year-old farewell.
Koeman wrote: “Still hard to understand that you will not play for Barcelona anymore.
“Thanks for everything you have done for our club, Leo. I really enjoyed the full season we worked together.
“I am impressed by your work ethic and desire to win; it makes you the best player in the world. For now, I wish you and your family the best!”
The statement partly reads: “Despite FC Barcelona and Lionel Messi having reached an agreement and the clear intention of both parties to sign a new contract today, this cannot happen because of financial and structural obstacles (Spanish Liga regulations).
Messi is now on the verge of completing a stunning move to Paris Saint-Germain.
The Argentina captain will sign a two-year deal with the Ligue 1 giants, with an option of one more year.