Jorgensen, recognised for his ability with the ball at his feet, has attracted the attention of the Blues' hierarchy, who are looking to find a goalkeeper who aligns with Enzo Maresca's new system.
At present, Robert Sanchez has been promoted to the role of Chelsea's starting goalkeeper, filling in for Petrovic, who is sidelined with an injury.
Reports earlier this week suggested that the Blues are also looking to offload the Serbian this summer despite only signing him at the start of last season.
Chelsea paid around £13.5m to acquire Petrovic from MLS outfit New England Revolution, and he made 23 appearances in the Premier League last term, producing 75 saves and keeping five clean sheets.
Chelsea closing in on Jorgensen signing
Fabrizio Romano reports that Chelsea and Villarreal are negotiating a transfer fee of between £17m to £21m for Jorgensen, who distinguished himself as one of the top ball-playing goalkeepers in La Liga last season.
The report adds that the Blues have already made contact with the 22-year-old, and have agreed personal terms with him.
The Swedish-born Dane is keen on a move to Stamford Bridge and previously admitted that being linked to a club like Chelsea was an honour for him.
It is understood that Chelsea aimed to act swiftly to prevent a potential hijack of the deal, as Roberto de Zerbi's ambitious Olympique Marseille had also shown interest in the player.
This comes after reports last week suggested that the West Londoners saw their first bid for the shot-stopper rejected by Villarreal.
Negotiations proceeding smoothly for Jorgensen deal
The Yellow Submarine value the player in the region of £30m but are believed to now be willing to listen to offers of around £21m.
It is said that two clubs are now negotiating the payment structure and will finalise the deal once for Jorgensen once they agree to the payment terms.
The discussions are expected to be smooth given the good relationship Chelsea and Villarreal have built, following last summer's transfer of Nicolas Jackson, during which the Blues paid above his release clause to secure him.
Jorgensen made 44 first-team appearances for Villarreal and cemented his role as the club's number-one goalkeeper last season, helping them finish eighth in La Liga.
Kepa Arrizabalaga also returned to Stamford Bridge this summer following his loan spell last season, and reports suggest the club hopes to sell the Spaniard ahead of the new season, with Al-Ittihad showing interest in the 29-year-old.