The former England captain is currently entrenched in preparation for next season with Rangers as he aims to challenge defending champions Celtic in the Scottish Premiership.
He has already secured the signings of Jordan Jones, Jake Hastie, Greg Stewart and Steven Davis and Gerrard is expected to utilise his Liverpool connections to make a fifth signing in the form of a loan deal for Sheyi Ojo.
Rangers will be keen to improve on what was a solid first season in charge for Gerrard.
They finished second in the league, earning themselves a spot in this season’s Europa League but were disappointingly eliminated from both the League Cup and Scottish Cup by Derek McInnes’ Aberdeen.
Rangers boss Steven Gerrard has rejected an approach from Derby to replace Frank Lampard (Image: GETTY)
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Now managers, Gerrard and Lampard both made over 100 appearances for England (Image: GETTY)
In similar fashion to reports linking Lampard with the Chelsea job, Gerrard has been tipped as a future Liverpool boss himself but recently underlined his commitment to Rangers.
“Today, I am very happy to be at Rangers and happy to do this job,” he said last November.
“I want to give the best of myself for Rangers.
"But nobody knows the future...Liverpool is a very special place for me. One day, maybe it will happen...or not."
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Frank Lampard to Chelsea WILL happen says Harry Redknapp
Chelsea legend Frank Lampard is expected to return to the club as their new manager (Image: GETTY)
While the news will come as a welcome boost for Rangers, it will be a blow for Derby who will need to replace Lampard should he return to Chelsea.
Lampard impressed during his debut season in management at Pride Park, guiding his side to the Championship play-off final where they lost 2-1 to Aston Villa.
Another potential candidate linked with Lampard's current job is his former team-mate John Terry who is Villa’s assistant coach.
Terry has made no secret of his ambitions to move into management and he could view the Derby job as the perfect way to start his career in the same way that Lampard did.