The 22-year-old defender has attracted attention from a host of top European clubs after a series of commanding performances both domestically and in Europe this season.
Red Devils boss Sir Alex Ferguson has been credited with an interest in bringing Mangala to Old Trafford, and is likely to pass on his recommendation to his successor, David Moyes, who takes over first-team affairs at Manchester United from July 1.
Bayern Munich and AC Milan have also been mooted as admirers of the France U21 international, and could make rival bids for his services when the transfer window reopens.
However, according to Portuguese newspaper A Bola, Dortmund boss Jurgen Klopp has identified Mangala as a priority signing for the Champions League finalists this summer.
Rated at around £17million, Mangala has continued to blossom at Estadio do Dragao, and is on course to win his second consecutive Primeira Liga title with Vitor Pereira's side this year.