The former midfielder is expecting a 1-1 draw between the two sides.
Sunderland manager David Moyes acknowledges fans at the end of the match
The two sides meet at the Stadium of Light on Sunday afternoon in their second games of the new season.
They head into the fixture after enjoying mixed opening weekend clashes against Manchester City and Stoke respectively.
Middlesbrough manager Aitor Karanka before the match
David Moyes’ Black Cats were unfortunate losers at the Etihad courtesy of a late Paddy McNair own goal, while Aitor Karanka’s team enjoyed a solid start by securing a point against the Potters.
Both teams will be keen to get their first win on the board as a result, especially against their rivals, but Redknapp is predicting a tight draw.
“I think it’s a battle between the two forwards, Defoe and Negredo,” he told Sky Sports.
“I’m going to go for a draw. I think it’s going to be a tight game, I can see a 1-1. I’m going with Negredo to keep up that good form and get the first goal.”
Sunderland's Jermain Defoe celebrates scoring their first goal
It will certainly be interesting to see which of leading strikers Negredo and Jermain Defoe comes out on top in this game.
Both enjoyed goalscoring starts to the season and will very much be key to their sides’ hopes of staying away from the relegation zone.
And in a game that is likely to be a tight one as Redknapp predicts, whoever has the better day is likely to be key to determining who comes away with the points.
Middlesbrough's Alvaro Negredo celebrates scoring their first goal