The Bundesliga club initially rejected an offer of around €20m (£14m) for the starlet whom they had signed for £1m from Greuther Fürth only a season ago, but are now expected to agree to the deal which also includes significant amount in add-ons.
Mourinho, who is preparing the champions for the Community Shield meeting with arch rivals and FA Cup winners Arsenal on Sunday, confirmed that Blues are roaming the transfer market for new additions in the squad.
“We are trying to sign a left-back,” he said. “We have only one [César Azpilicueta]. We are trying.”
Te Blues have tracked the Ghana international for the entire summer after being alerted to the youngster’s talent by their former manager, Avram Grant, who now manages African side.
The Portuguese boss considers the 21-year-oldRahman as someone who can challenge Cesar Azpilicueta for a starting place in the Chelsea XI and prove to be a star for the longer term at the West London club.
Baba was part of the squad that qualified for the final of the Africa Cup of Nations earlier this year, losing on penalties to Ivory Coast.
Having started his career in Ghana at Accra-based Dreams FC, Rahman has enjoyed a spectacular rise in European after joining Greuther Fürth from Asante Kotoko in 2012. He is now regarded as one of the best young defenders in Europe and was nominated as the best left-back in his first season in the Bundesliga, losing out to Bayern Munich’s Juan Bernat.
Premier League clubs Arsenal and Manchester City were among the other clubs to have expressed an interest in signing him earlier this summer, while Atlético and Roma had also asked to be kept informed.