The Spanish star joined the Hoops from Real Madrid in August and signed a four-year deal with the West London side.
But it has been a disappointing start to life in England, with Mark Hughes' men currently bottom of the Premier League.
Rangers have taken just four points from their opening 11 matches and are yet to register their first win of the campaign.
But Granero told Sky Sports: "I assure every supporter - I want to be here.
"I have heard some of that [speculation], but it's not true.
"I came here to face challenges and I'm not the kind of footballer who runs away when things are not going very good.
"I like being here. I want to push the team to the place they deserve."