Di Maria has yet to complete his long-awaited move to Old Trafford but Real manager Carlo Ancelotti revealed on Sunday that he has already said his goodbyes to his colleagues.
And Alonso has taken to Twitter to express his gratitude to Di Maria for the role he played in Madrid's Champions League final triumph over city rivals Atletico, while wishing him well at his prospective new employers.
"Thanks for everything, Fideo," the former Liverpool midfielder wrote. "I wish you the best - even at Man. Utd.
"I will never forget the extra-time zig-zag [run] in Lisbon."
Di Maria was linked with a move away from the Santiago Bernabeu last summer, following the arrivals of Gareth Bale and Isco from Tottenham and Malaga, respectively.
However, the Argentina international stayed in the Spanish capital and proved Madrid's key player in their 4-1 Champions League final win over Atletico, slaloming his way into the area before unleashing a shot that Thibaut Courtois could only palm into the path of Bale, who headed home to put Los Blancos ahead and break their city rivals' resistance.