Lampard guided the Sky Blues to the Premier League this summer, winning the Championship title in the process and ending a 25-year wait for top-flight football at the club.
That success has raised his profile considerably, with other clubs, including Fulham, credited with interest in the 47-year-old.
Talks over fresh terms at Coventry are now under way, and have been described as positive, with hope growing inside the club that an agreement can be reached before the new season begins.
Lampard took charge of Coventry in November 2024, when the club sat 17th in the Championship, just two points above the relegation zone. He won 16 of the remaining 29 games that season, lifting Coventry to fifth and into the play-offs, where they were beaten 3-2 on aggregate by Sunderland in the semi-finals.
The following season delivered the title itself, with Lampard's side winning 28 league matches — the most Coventry have ever managed in a single campaign.
Speaking after promotion was confirmed in April, Lampard reflected on the scale of the challenge ahead.
"There's a lot of work to do because we know the step up it will be for the football club. That's something we have to work on quickly now because of where we're at," Lampard said.
"We have to be ambitious. I know what the Premier League is and it's going to be a challenge.
"We can enjoy the moment for the next two weeks but of course we have to work behind the scenes to ensure we go up in the right way."
The former England midfielder began his managerial career at Derby County before two spells at Chelsea and a stint at Everton, but his work at Coventry has been widely regarded as the most complete project of his coaching career to date, making a new contract a priority for a club keen to build stability around the man who delivered their return to the top flight.