Lalu also said that his party will not leave coalition in the state.
RJD leader Tejashwi Yadav, who was under pressure to resign after the CBI registered an FIR against him for alleged corruption, may quit as Bihar Deputy CM, sources said on Friday.
Congress President Sonia Gandhi spoke to Bihar Chief Minister Nitish Kumar and RJD chief Lalu Prasad Yadav over phone on the ongoing rift between two major players in Bihar's Grand Alliance.
According to sources, after Sonia's intervention to save the Mahagathbandan it was decided that Tejashwi will submit his resignation after presidential poll scheduled to be held on July 17.
Though Nitish Kumar has not publicly spoken on this matter but his party JDU has maintained that mere explanation by Tejashwi on charges against him is enough and an action will be taken for sure.
His silence has given rise to speculation of cracks in the Bihar's Grand Alliance government-- comprising JDU, RJD and Congress.
Sources said demands of resignation of Tejashwi, seen as Lalu Prasad's political heir, could trigger dramatic developments in Bihar's ruling alliance. Worried about JDU-RJD's strained relationship, Sonia decided to intervene.
RJD till now has stood firmly behind Tejashwi and dismissed the BJP's demand for his resignation.
After Nitish asked him to come clean, Tejashwi has dubbed the corruption charges against him a "conspiracy" hatched by the BJP brass.
The BJP has repeatedly asked Nitish Kumar to sack Tejashwi Yadav and end the alliance with the RJD.
Tejashwi, facing an inquiry by the CBI, also made light of the allegations against him, saying they relate to a period when he was 14 years old.
Lalu Prasad, his wife and former Chief Minister Rabri Devi and their son Tejashwi Yadav have been named accused in a CBI case related to the transfer of prime land in Patna to the family by two businessmen allegedly in return for licences granted to run hotels in Ranchi and Puri when the RJD chief was the Railway Minister.
(With inputs from agencies)