The 26-year-old World Cup winner was reported to be among United boss Louis van Gaal's key transfer targets.
"Of course when the big clubs are interested, and Manchester United is one of the biggest clubs in the world, it's an honour," said Hummels.
"I decided not to make the move this year. I decided I wanted to stay here."
Hummels, who has two more years on his Dortmund contract, was part of the Germany team that won the World Cup in Brazil last year.
He has also secured two Bundesliga titles since joining Dortmund permanently from Bayern Munich in 2009 after an initial loan move.
Borussia Dortmund defender Mats Hummels, who has been linked with a move to Manchester United, says he is staying at the club for another year.