Lampard's return to Stamford Bridge as the successor to Maurizio Sarri is reportedly close despite his single season of experience with the Rams.
And former England team-mate Gerrard is said to be on Derby's list of targets should Lampard's move to Chelsea be completed.
The Rangers manager, however, insisted he is not looking to leave the Glasgow giants after helping to narrow the gap on Celtic last term.
"Yes, I'm aware of it but there's nothing to say on it," Gerrard told Sky Sports of the speculation.
"I'm very happy here, it's a privilege to be the Rangers manager. My focus is on the up and coming season.
"It's very similar to when there's noise around players. I ask the players to stay focused on the job and that is what I will continue to do. There is nothing really to add to that.
"Nothing has changed in my mind. I was very lucky and appreciative of the opportunity I got 12 months ago.
"I'm delighted to be at Rangers, managing one of the biggest clubs you can manage, so nothing has changed in terms of my focus."
Rangers finished second behind Celtic last term and lost to Aberdeen in the quarter-finals of the Scottish Cup.
Lampard's Derby, meanwhile, finished 6th in the Championship, clinching a play-off spot by one point, but ultimately lost out to Aston Villa at Wembley.
John Terry, Lampard's former Chelsea team-mate, celebrated in the opposing dugout and signed a contract extension last week to stay as Dean Smith's assistant head coach at Villa Park until 2021.
But Gerrard insists he is happy with life north of the border, as Rangers look to overhaul Celtic's dominance in Scotland next season following the departure of Brendan Rodgers to Leicester in February.
The Hoops completed an historic triple treble last term and will be aiming to consolidate their position of power under Neil Lennon.
Glasgow's two biggest clubs are set to clash on August 31 for their first encounter of next season.