Herrera's United contract expires at the end of the season and it is believed he has lined up a deal with French champions PSG.
United hadn't commented on Herrera's future, but the 29-year-old Spaniard posted a goodbye message to fans via the club's Twitter account on Saturday.
"There is red in my heart, I knew it from the first time I played here and in the moment I started to wear it," said Herrera, who has also been linked with Arsenal, Juventus and Inter Milan.
"Every time I represented this club, in every game, in wins and losses, even when I couldn't help from the grass, I understood what this club means.
"I am going to remember each of the almost 200 matches that I have played with this jersey. Because playing for the greatest club in England, has been a true honour. Thanks for these five amazing years."
Herrera, twice capped by Spain, joined United from Athletic Bilbao in 2014 and has gone on to make 189 appearances for the club, winning the FA Cup, League Cup and Europa League during his time in England.
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