The former United player will return to Old Trafford to face the Welshman, who was placed in charge of the club's final four Premier League games.
The Black Cats, who currently reside one place above the relegation zone on goal difference, are unbeaten in their last three fixtures.
"I always thought Ryan would eventually go on to manage a team," Brown told Sunderland's official website. "I'm sure he's thriving on it and looking forward to the next few games ahead.
"United will definitely be up for the game, as will the crowd. We've got to try and drain that and go out to do what we've been doing over the last few weeks."
United are seventh in the table.