Jospin made the announcement on France's RTL Radio and said he would not support Socialist rival Segolene Royal, who has a massive lead in public opinion polls, a Financial Times correspondent in Paris reported.
However, Jospin said he would refrain from making any statements to damage fellow Socialists' poll chances.
"As I could not bring the party together, I have decided not to divide it," he said.
Jospin was attempting a political comeback after being routed in the 2002 presidential elections, the newspaper said.
Socialist presidential contenders have from Saturday until Oct. 3 to declare their candidacies. Party members will vote in November to decide who represents them in next April's election.
Notable deaths of 2014 [PHOTOS]