With his close friend and former England team-mate Frank Lampard poised to quit Derby to become the new Chelsea manager, Gerrard is among the bookies' favourites to replace him at the Championship club.
But Gerrard, who signed a four year contract when he became Rangers manager in the summer of 2018, insists he remains fully focused on the challenges ahead at Ibrox.
"Yes I'm aware of it (the speculation) but there's nothing to say on it," Gerrard told Sky Sports News.
"I'm very happy. It's a privilege to be the Rangers manager and my focus is on the coming season.
"It's very similar to when there is noise around players. I ask them to stay focused on the job and that's what I'll continue to do. There's nothing really to add to it.
"I was very lucky and appreciative of the opportunity I got 12 months ago. I came in very focused in season one. Nothing has changed in my mind.
"I'm delighted to be the Rangers manager, I'm managing one of the biggest football clubs you can manage so nothing has changed in terms of my focus."
Gerrard is in Portugal with the Rangers squad this week as they step up preparations for the new season. He confirmed that Charlton midfielder Joe Aribo was undergoing a medical on Monday and is expected to become Rangers' seventh summer signing.