Jeffren, 25, is widely expected to leave Estadio Jose Alvalade in search of first team football and was recently linked with a switch to Liverpool.
The Reds, however, failed to step up their interest in the January transfer window, but he has now received two offers from France.
According to O Jogo, both Marseille and Saint Etienne are interested in signing the player on loan until the end of the season.
Nevertheless, Sporting Lisbon chiefs are not keen on such an arrangement and would only consider outright sale due to their difficult financial situation.
Jeffren Suarez joined the Lions in a €4 million move from Barcelona in the summer of 2011, but has not exactly justified the money invested in him.
He has made just 20 Primeira Liga appearances for the club, and scored 3 goals in the process.