Goal understands the 19-year-old wants to leave west London when his current deal expires in June to link up with the Ligue 1 champions in the French capital.
He made three appearances during pre-season ahead of the 2018-19 campaign but is yet to make his full senior debut in a competitive match.
Maurizio Sarri has included Bulka in his squad for Europa League away trips during the season, but a lack of minutes at any level has seen the shot-stopper look to find pastures new.
Competition from Jamie Cumming, who this season renewed his contract until 2021, and Nathan Baxter, who was named Player of the Year and Young Player of the Year while on loan at League Two outfit Yeovil Town this season, meant Bulka was not willing to accept an extension to his current deal.
And PSG have moved quickly to beat off competition from a host of European clubs to bring the Poland youth international to Parc des Princes.
He will provide competition for Gianluigi Buffon and Alphonse Areola in Paris while it is not known whether Kevin Trapp - currently on loan at Eintracht Frankfurt - will return to the club.
Chelsea's youth academy is increasingly being looked at as one of the world's best breeding grounds for young talents, and as such Europe's biggest clubs are continuously attempting to poach players from the Cobham Training Centre.
As such, talks are expected to take place in the coming weeks with a host of young talents regarding their futures.
The likes of Juan Castillo, Joseph Colley, Geroge McEachran, Bradley Collins, Josh Grant, Jared Thompson and Tariq Uwakwe all have contracts which expire in June but could yet be persuaded to stay with the Premier League outfit.