Portuguese newspaper A Bola claims the Stamford Bridge club are keen to sign the 19-year-old midfielder, who has a €30m release clause in his Benfica contract.
Jose Mourinho has been tipped to sign a Benfica central midfielder - but most reports linked the new Blues boss with a move for former-Chelsea youngster Nemanja Matic.
But the latest reports, also carried by talkSPORT, suggest the teenage starlet could be targeted by Mourinho.
Gomes arrived on the Liga Sagres scene last season, after an impressive campaign with the reserve side.
Following his call-up to the first-team squad, he made seven appearances last term and featured in the Champions League against Barcelona.
The Benfica midfielder only signed a new contract with the Portuguese club in January 2013, a deal that runs until 2019 and bumped his release clause up to €30m.
The report claims Chelsea don't want to go anywhere near that fee, and hope a deal can be agreed for a much lower price.
The speculation linking Gomes with Chelsea comes on the same day as Valencia's interest in Blues midfielder Oriol Romeu.
The former-Barcelona midfielder is another highly-rated young player, but he spent much of last season on the sidelines with a knee injury. Celta Vigo are also reportedly keen to take him on loan.