The Chelsea hero, 46, is reportedly among the leading candidates for the position after Robins was dismissed earlier this month following a poor start to the season.
Lampard, who has previously managed Derby County, Chelsea, and Everton, is understood to be keen on the role despite not applying for it, according to The Sun.
The former England international has experience in the Championship, having guided Derby to the play-off final in 2019.
Ruud van Nistelrooy, the former Manchester United striker, is also a strong contender, The Sun reported.
The Dutchman, 48, recently served as interim manager at United, where he secured three wins and a draw following Erik ten Hag’s dismissal, before being replaced by Ruben Amorim.
Lampard has been out of management since a difficult interim spell at Chelsea last season, where he won just one of 11 games. He has since been working as a pundit but recently expressed his desire to return to management, even hinting at future ambitions with England.
He said: "As an English player who played 100-plus times, and an English person who's very proud – of course, the England set up is something... I never dreamed of playing as many times for England, let alone now as a coach.
“So, now as a coach, I think I would be crazy to sort of say, ‘Oh no, that would never interest me.’"
Coventry, currently 17th in the Championship and just one point above the relegation zone, is also considering Wycombe manager Matt Bloomfield for the role.
Van Nistelrooy reportedly threw his hat into the ring shortly after Robins’ departure, but Lampard’s extensive experience could make him a front-runner for the job.