The Evening Standard claim that the Premier League champions are "monitoring" the defender.
Chelsea are reportedly looking to sign another centre-half in the summer.
And the club "have been admirers of Lascelles since 2016", according to the Standard.
Lascelles signed a new deal last October keeping him at United until 2023.
The Derby-born player, signed from Nottingham Forest in the summer of 2014, took the captaincy in 2016 following the departure of Fabricio Coloccini.
Lascelles has impressed this season in the heart of Rafa Benitez's defence.