The Blues are facing a battle to keep their current number one Thibaut Courtois in the summer transfer window.
The Belgium international has 12 months left to run on his deal with the west London side but is open to a return to Madrid.
Courtois spent three seasons at Atletico Madrid between 2011 and 2014 before he return from his loan spell to replace Petr Cech at Chelsea FC.
The Belgian shot stopper has been regularly linked with a move to Real Madrid and los Blancos are thought to be interested in signing a goalkeeper.
Brazil international Alisson is thought to be a target for Real Madrid as well as Chelsea FC in the current transfer market.
Daily Record reporter Castles shed light on Chelsea FC’s interest in the South American goalkeeper this summer.
“Chelsea have made an inquiry for Alisson,” Castles told the Transfer Window podcast,
“It isn’t clear whether they are trying to find out if he is going to Real Madrid or they are willing to spend the £70m it would take to sign Alisson.”
Chelsea FC finished in fifth place in the Premier League table last season to miss out on a Champions League spot for the second time in three seasons.
The Blues haven’t won the Champions League title since 2012 when the west London side beat Bayern Munich on penalties.
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