Tomori, who has been at AC Milan since January 2021, has his contract expiring in 2027 and is among the players who could leave San Siro this transfer window.
Former Aston Villa chief executive Keith Wyness confirmed the interest in comments to Football Insider.
"I get the sense that Lampard is working hard behind the scenes to get the deal done. Coventry City will need something to strengthen themselves in some way," he said. Wyness was quick to note, however, that convincing Tomori to join a newly-promoted side aiming simply to stay in the Premier League would not be straightforward.
Coventry returned to the top flight this summer for the first time in 25 years after winning the Championship title under Lampard, whose reputation has been transformed by reviving a club that had fallen as low as the fourth tier earlier in the decade.
The Sky Blues are widely expected to invest significantly in the squad over the coming weeks as they prepare for the step up in quality, with Lampard's connections across English and European football giving the club access to players who might not otherwise consider a move to Coventry.
Tomori's situation at Milan adds an extra layer of intrigue, with the defender facing an uncertain role under new head coach Ruben Amorim as his contract enters its final years. Whether he would be tempted by regular Premier League football at a promoted club over a more peripheral role at one of Serie A's biggest clubs remains to be seen, but Lampard's personal relationship with the player, forged across two different clubs, gives Coventry a genuine point of leverage as they attempt to turn interest into a concrete approach this summer.
The England international's experience of both Serie A and Premier League football would also represent a significant upgrade in pedigree for a Coventry backline being rebuilt for the rigours of the top flight.