The Armenia international moved to the north London side in a swap deal from Manchester United in the January transfer window.
Mkhitaryan secured a switch to Arsenal as Chile international Alexis Sanchez completed a controversial switch to the 20-time English champions.
The 29-year-old struggle to hold down a regular starting spot under Jose Mourinho despite the Portuguese head coach signing the Armenian playmaker.
Mkhitaryan scored in a 2-1 loss to Manchester United last month to take his tally to three goals and five assists in 17 games since his move to Arsenal.
Writing on his personal blog One Hour Behind last week, Mata sent a message to Mkhitaryan following his move to the north London club.
“In this game I could see Mkhitaryan again, to whom I wish the best,” Mata said.
“He scored a good goal that he didn’t celebrate, and Old Trafford also showed its affection to him :-).”
Mata moved to Manchester United in a £37.1m deal from Chelsea FC in the 2014 January transfer window.
The Red Devils will take on Mata’s former club Chelsea FC in the FA Cup final at Wembley later this month.
Manchester United are in second place in the Premier League table and four spots ahead of the north London side.
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