The newly promoted Premier League club have agreed a deal comprising £15.4m up front and up to £1.7m in add-ons, and the Switzerland international is expected to sign a four-year contract.
The 22-year-old was reportedly won over during talks with the former Chelsea boss and the club's recruitment team, and reports in Germany suggest the fee would make him the most expensive signing in Coventry City's history.
The defender, who joined Frankfurt from Young Boys in 2024, established himself over the second half of last season, starting 15 of the club's final 18 Bundesliga matches on his way to 29 appearances in all competitions. A towering presence who is renowned for his aerial strength, he can also deputise at right-back, adding further value to a Coventry back line preparing for the step up in level.
Amenda travelled to the World Cup with Switzerland this summer and watched on as his country reached the quarter-finals, without featuring himself.
Amenda would become Coventry's third arrival of the summer window, following winger Loum Tchaouna's move from Burnley and midfielder Frank Onyeka's permanent switch to the club after his successful loan spell from Brentford.
Attention will then turn to the goalkeeping position. Brighton's Carl Rushworth remains the first choice, but with no agreement reached so far, Chelsea's Filip Jorgensen is also under consideration.
There is plenty of optimism building around the CBS Arena ahead of the club's first top-flight campaign in 25 years. Lampard committed his future with a renewed contract earlier this summer, and his side have begun their preparations in earnest, opening pre-season with a narrow behind-closed-doors friendly loss to Wimbledon, with Northampton Town and Espanyol to come.
Landing Amenda would represent a significant statement of intent from the Championship winners, who are determined to give themselves every chance of establishing Premier League football back in Coventry after a quarter of a century away.