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The Senegal striker, a Muslim, told club officials he was not prepared to promote Wonga, a firm which offers short-term, high-interest loans.
Islamic law forbids borrowing or paying money with interest.
However, the 28-year-old did offer to wear an unbranded shirt or one bearing a charity logo instead.
Other sports teams have made concessions to the faith of their Muslim players, with South Africa cricketer Hashim Amla allowed to wear shirts without the logo of team sponsor Castle Lager because of the Islamic prohibition on drinking alcohol.
The BBC quoted sources saying Cisse's refusal to wear the sponsored shirt had left him in a "strained" relationship with the Premier League side.
Cisse's Newcastle team-mates Cheick Tiote and Moussa Sissoko are also Muslim, but have told the club they have no issue with wearing the sponsor's logo.
Speaking in June, PFA deputy chief executive Bobby Barnes told BBC Sport: "We're all aware that clubs need to generate revenue and sometimes have to use a wide range of companies.
"However, if someone feels very, very strongly that it's not compatible with their beliefs, then some sort of solution should be found."
Cisse joined the Magpies in January 2012 and has scored 26 times in all competitions.
