The 29-year-old met the Red Devils’ latest acquisition after Brazil beat Serbia 2-0 at the World Cup on Wednesday.
Fred was an unused substitute in the clash, but the pair caught up at full-time.
United’s second signing of the summer took to Instagram to reveal Matic had given him his match shirt.
Fred completed his move to the Red Devils last week as part of a £52million transfer, joining on a five-year deal.
(Image: Simon Hofmann – FIFA/FIFA via Getty Images)
It is thought the former Shakhtar Donetsk man will slot in alongside Matic in midfield and provide healthy competition for Paul Pogba.
“I spoke to him after the game, he is a great player, he will bring quality to our team,” said Matic.
When asked of they can work together, the Serbian added: “We will see. I think we’ll understand each other very well.”