United and Forest will meet at Old Trafford on Sunday to play out their penultimate game of the Premier League season.
Anderson, 23, has been key for Forest this season, popping up with four goals and two assists in his 36 league games.
The midfielder's fine form has caught the attention of several clubs, including Manchester United and rivals Manchester City, ahead of the summer transfer window.
Speaking to reporters ahead of their game, Carrick was full of praise for Anderson, saying: “He's done well.
“I think he's a big part of their team. He offers so much and they've got a really talented and dangerous team.
“They've had a good season to get to the (Europa League) semi-finals and just fall short. But you can see obviously he is an important part of their team.”
Both Carrick and Anderson started their footballing careers at the Wallsend Boys Club on Tyneside.