The Blues could be in the market for a new stopper ahead of the 2020-21 campaign, with current number one Kepa Arrizabalaga struggling for form since arriving in a world-record deal.
Willy Caballero was the team's first-choice goalkeeper in the Premier League before the action was postponed in March, but the experienced Argentine is not thought to be in the running to be the number one next term.
According to The Sun, Frank Lampard's side have identified Dortmund's Burki as a possible arrival in this summer's transfer window.
The report claims that the Blues are lining up a £15m offer for the Switzerland international, who only has one year left to run on his contract at Signal Iduna Park.
Burki has kept 12 clean sheets in 33 appearances for BVB this season.