Chelsea made a world record attempt for Atletico Madrid goalkeeper Jan Oblak before signing Athletic Bilbao's Kepa Arrizabalaga.
The Times says Blues chiefs met Oblak's release clause only for the Atletico Madrid stopper to snub a move.
Slovenia ace Oblak, 25, replaced Courtois in the Spanish capital in 2014 as has been named in La Liga's team of the year twice.
The report adds that Atleti are prepared to offer the keeper an improved deal in reward for his loyalty which will push his buy-out fee to £223m.
Kepa, 23, began his Stamford Bridge career with a clean sheet as Sarri's side toppled Huddersfield 3-0.