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.
Justin Bieber crashes Drake Bell's album release party
Chipotle plans first price increase in 3 years