The Blues were willing to pay £89.4 million (€100 million) to buy out his Atletico contract as they sought a replacement for Thibaut Courtois, according to Duncan Castles at the Sunday Times (h/t Kate McGreavy for MailOnline).
Oblak chose to remain in Spain because he wants to play UEFA Champions League football, something Chelsea were unable to offer this term after finishing fifth in the Premier League last season.
The Slovenia international is regarded as one of the best goalkeepers in Europe. Oblak moved to the Spanish side in 2014 and helped the club win the UEFA Europa League last season.
Atletico's greatest strength is their defensive solidity and organisation. Squawka Football showed how impressive Oblak has been during his time with the club:
Diego Simeone's side finished second behind Barcelona in La Liga last season. The club has strengthened in the summer by bringing in Thomas Lemar, Rodri and Nikola Kalinic, leaving Atletico looking well-placed to challenge for the title.
Sports writer Andy West is impressed with their squad:
Atletico are keen to keep Oblak at the club. They want to increase his wages and his buyout clause in order to deter other admirers, per Cadena SER (h/t Football Espana).
After missing out on Oblak, Chelsea opted to spend big on Athletic Bilbao's Kepa Arrizabalaga. The 23-year-old has joined in a deal worth £71.6 million, per the Telegraph's Matt Law.
Kepa is a highly promising young goalkeeper who looks to have a great future ahead of him. He lacks the experience and authority of Oblak, but he has the potential to become one of Europe's best stoppers.
Chelsea manager Maurizio Sarri recently offered his view on his new signing, per Liam Twomey at ESPN FC:
Kepa must also cope with the pressure of being the most expensive goalkeeper in the world as he adapts to a new country and the Premier League.
He picked up a clean sheet on his Blues debut against Huddersfield Town on Saturday. However, he was rarely tested, per Goal's Nizaar Kinsella:
Losing Courtois was a blow to Chelsea ahead of the new season. While Oblak would have been a superb replacement, Kepa looks a strong choice who has a big future ahead of him.