Citing reports in Istanbul, the Portuguese newspaper claims that the Chelsea manager is exploring several striker options for the winter window - and Yilmaz is the latest name under consideration.
Ba could be set to leave Stamford Bridge this summer after struggling to break into the starting eleven since his move from Newcastle earlier this year. His start against Norwich was just his second Premier League appearance of the campaign so far.
Because the report claims Mourinho intends to strengthen his attacking options with the addition of the 28-year-old Galatasaray ace.
The Turkey international has been prolific throughout his Super Lig career, and top scored last season with 24 goals as Galatasaray won the league at a canter.
He had built up a promising partnership with former-Chelsea striker Didier Drogba in Istanbul, but Galatasaray have been poor so far this season - culminating with the departure of Fatih Terim earlier this term. He was replaced by Roberto Mancini.
Mourinho has three senior strikers at present - Ba, Samuel Eto'o and Fernando Torres - but he's been strongly linked with a number of top-tier forwards since his arrival at Stamford Bridge.
Despite the addition of Eto'o from Anzhi, the Chelsea boss has reportedly monitored Robert Lewandowski, Karim Benzema, Jackson Martinez and most recently, Yilmaz.