Jorgensen impressed after becoming a regular with the Spanish side last season, ranking second among all goalkeepers across Europe’s top five leagues for saves (143).
The 22-year-old is viewed as a player of high potential by Chelsea who are seeking to bring in competition for their number one shirt.
Chelsea’s interest comes despite a need to offload Kepa Arrizabalaga, who has returned from a loan spell at Real Madrid and is subject of interest from the Saudi Pro League.
There are also doubts over the future of Djordje Petrovic who could leave despite making 31 appearances in all competitions last season, with a new goalkeeper targeted to compete with Robert Sanchez for first-choice status at Stamford Bridge.
Chelsea are assessing multiple goalkeeping options but Jorgensen features highly on the club’s shortlist.