Chilwell has developed into one of the Premier League's best full-backs with his attack-minded style.
Lampard has struggled to settle on a left-back this season, using Marcos Alonso, Emerson Palmeri and Cesar Azipilcueta in that position.
The arrival of Chilwell would be an upgrade on their current options, and Johnson thinks the 23-year-old is ideal for Chelsea.
“I’ve said many times I am a fan of Chilwell,” Johnson told talkSPORT. “I like the way he carries himself.”
Ben Chilwell keeps the ball from Sadio Mane (Image: GETTY)
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“There’s no doubt he is a wonderful footballer but Chilwell is a natural full-back.
“It’s a hefty price tag, there’s no doubting that, but if [Chelsea] can get a deal for him that is reasonable then he’s a player they should try to get.”
Chelsea resume their Premier League season on June 21 with an away trip to Aston Villa.