Hughes was reported to be on the brink of quitting the City of Manchester Stadium club due to concern over his control on transfers, and at a time when owner Thaksin Shinawatra's future appears unclear.
The former Blackburn manager said: "There have been a lot of rumours flying around but I am not going anywhere and I don't anticipate going anywhere.
"There is a job to do here and I am looking forward to it."
He told club website: "There is speculation around the club and that has been prevalent since I joined the club but from my own point of view I am very focused on what I am about and what I aim to achieve here and that means success on the pitch.
"Nothing whatsoever has changed in that respect and the football operation hasn't changed since I signed for the club. Nor has my relationship with Garry Cook and his team. We get on really well and continue to speak on a daily basis.
"I am the guy that makes the decisions in relation to the football, and they make the decisions in relation to the running of the club."