The Bundesliga club have made the Spanish forward their main target during this summer’s transfer window, despite only joining The Blues last summer.
The 25-year-old scored 11 goals in 31 Premier League games last season following his £58m move from Real Madrid.
According to Talksport, Dortmund are ready to make a move for him.
However, they could be put off by the rumoured £45m fee Chelsea want for Morata, which could see them instead for Werder Bremen’s Max Kruse, who would come at a cheaper price.