Evra, who joined West Ham on a free transfer in February 2018, was on the books of United from 2006 until 2014.
Carrick also moved to the Red Devils in 2006 and has retired from professional club football at the end of this season.
Former France international left-back Evra, 36, who is out of contract at West Ham this summer, has sent an emotional message to Carrick on Twitter.
What a man. On and off the pitch he is a really great guy who was fantastic to play with. @carras16 we will miss you. Have a great retirement.— Patrice Evra (@Evra) May 13, 2018
He whispers in my ear 'I love this game' ! ☺ pic.twitter.com/H23RtASYZY
Carrick is one of the best and most underrated footballers in the Premier League, but those who have played with him know his quality and calibre.
The former England international midfielder was successful at West Ham, Tottenham and United, and had a glorious playing career.
Evra has been equally successful in his playing career, and it will be interesting to see if West Ham hand the 36-year-old former Juventus and Marseille left-back a new contract this summer.