The two Premier League clubs are expected to be in the market for a goalkeeper at the end of the season.
Manchester United are in talks with David de Gea over a new contract on reduced terms, but they still want to bring in a serious competitor for his place in the team.
Chelsea are not convinced about either of the options they have in Kepa Arrizabalaga and Edouard Mendy and are looking for a new number one.
And according to the Swiss daily Blick, Kobel has emerged as an option for both Premier League giants.
The 25-year-old has been the undisputed number one at Dortmund this season and has impressed several observers.
His exploits have turned the heads of both Premier League clubs and they have his name on their shortlist of targets.
German champions Bayern Munich also have their eyes on the Switzerland international as the long-term replacement for Manuel Neuer.
But for the moment, Kobel is focused on the ongoing season and will tackle questions about his future only in the summer.
