The information emerged on the sidelines of a meeting of The Left's leadership in Berlin, the first at which Lafontaine has been present since his operation in November for prostate cancer. Speculation has been rife for weeks over Lafontaine's political future.
Sources say Lafontaine, who is from the state of Saarland, will not campaign for another term as leader at the party's conference in May. It signals the end of one of the most remarkable and controversial political careers in German politics.
Once the leader of the centre-left Social Democrats (SPD), Lafontaine took the helm of the hard-line socialist Left party in 2007 after it was formed by disgruntled western German trade unionists and members of the successor to the East German communist party.
He has been instrumental in helping the socialists establish themselves in western Germany, but his methods have irked many easterners.
In the wake of Lafontaine's illness, a leadership fight broken out between different camps of the party – the so-called "realists" and the "fundamentalists." Lafontaine is considered a member of the latter group, which focuses on being a vocal voice of the opposition.
The realists, many of whom are in eastern Germany, have been more interested in compromise and entering state governing coalitions with the Social Democrats.
"No one is irreplaceable," Dietmar Bartsch, the party's outgoing general secretary told the Saturday edition of the Saarbrücker Zeitung.
Bartsch is considered a member of the realist camp and recently lost a bruising intra-party battle where he was accused of disloyalty to Lafontaine.
"At some point, as it is with everyone, Oskar Lafontaine will not be in the first row anymore," he said.