Carrying reports from Spain, the newspaper claims that the 20-year-old former-Manchester City youth team star has emerged as a target for the Stamford Bridge club.
Chelsea scouts have been watching Suarez in action for Sevilla, where he is currently on loan from Barcelona.
Sevilla's agreement with Suarez is for a two-season loan, which means Chelsea would not be able to sign the youngster until the summer of 2016 at the earliest.
Barcelona allowed Suarez to join Sevilla after signing Ivan Rakitic from the Andalusian club just before.
Suarez joined Manchester City from Celta Vigo in 2011 but failed to make a single Premier League appearance for the Citizens. He was a star in the reserve team, winning the Young Player of the Year award in 2012.
But such is the spending power at Manchester City, he found it hard to break past the likes of Samir Nasri and David Silva. As a result, he moved back to Spain to join Barcelona B in 2013. The deal could be worth up to £8.1m with Suarez penning a four-year contract.
Chelsea transfer news
Young player policy
The Spanish under-21 international was a target for Chelsea in the summer of 2011 before he moved to City, and the Blues are once again keeping tabs.
Chelsea's transfer policy seems to include a concerted attempt to sign up the best young players in the world, with a view to loaning them out and potentially making a profit.
They currently have 26 players on loan around Europe, and have used the strategy in the past to make serious profits on Kevin de Bruyne and Romelu Lukaku.