Lampard left Chelsea at the end of last season after taking over as the club's interim manager in April.
The Blues legend endured a difficult second stint at the helm as he could only guide Chelsea to one win in 11 games.
Lampard - who is currently without a job - revealed his aim of bringing Rice to Stamford Bridge during his first spell as Chelsea manager.
"I wanted to bring Declan Rice to Chelsea when I was there as a coach before, he was my top target," he told Steven Bartlett's Diary of a CEO Podcast.
"I was like, this kid Declan is going to be the captain of Chelsea for the next 10 years".
READ MORE ON CHELSEA
Chelsea close to Lukaku agreement as Pochettino attempts to finalise pre-season squad
Spurs interested in Conor Gallagher, but midfielder heading to US for Chelsea pre-season
Rice was linked with a return to Stamford Bridge in 2021 after being released by the club in 2015.
But the midfielder turned down Chelsea's advances to remain at West Ham where he went on to become club captain, lifting the Europa Conference League title in June.
With a move to Arsenal in its final stages, Rice's connections with Chelsea appear to be all-but over.
The Gunners agreed a £105m deal with West Ham for the transfer of the England international but getting the move over the line has been a drawn-out process.
Most read in Football
Alli reveals childhood trauma, Henderson considers Saudi offer, Rice delay angers West Ham
Chelsea transfer news LIVE: Lukaku agreement close, Cherki bid, Caicedo hails Blues
Arsenal transfer news LIVE: 'Official' Timber photos leak, Rice deal further delayed
Man United transfer news LIVE: Hojlund part-exchange offer made, Onana talks continue
Fans have become impatient at the snail's pace at which the deal appears to be moving with reports suggesting the hold up is due to Arsenal's lawyers approving the final wording of the deal.
But Arsenal fans may not have to wait much longer for confirmation of the transfer.
The club are hopeful of concluding the deal before jetting out to the United States this weekend, for the second leg of their pre-season tour.