The Blues are currently uncertain about the future of Mason Mount, whose contract is set to expire next summer.
The 27-year-old has not shown any inclination to extend his contract, and there is a possibility that he may be sold when the transfer window reopens this summer.
In light of this situation, The Sun claims that Chelsea are preparing to sign the Brazil international as a possible replacement for Mount.
Pereira has been in excellent form for the Cottagers this season, contributing eight goals since arriving from Manchester United at the beginning of the campaign.
The West Londoners have been impressed with his progress and are considering a transfer for a reported fee of around £35m. It is also rumoured that Pereira would be inclined to accept the transfer offer.