Rice is all but set to join Arsenal from West Ham United in excess of £100m in the coming days.
The 24-year-old was released as a youngster from the Chelsea academy and he has gone on to blossom at the Hammers.
Rice skippered West Ham United to Europa Conference League glory back in June but that triumph over Fiorentina looks likely to be his final act for the club.
Lampard has had two spells as Chelsea manager, with his second stint arriving in April as an interim replacement for Graham Potter.
Lampard, who managed Chelsea between 2019 and 2021 before returning for the stint as caretaker boss earlier this year, told the Diary of a CEO podcast: “I wanted to bring in Declan Rice.
“I was like ‘this kid is going to be the captain of Chelsea for the next 10 years’. It didn’t happen, anyway, it is hard to dissect people’s work.”
