RJD has also offered one out of the 40 seats in the state to another Congress ally NCP.
The development comes after an old ally LJP walked over to the BJP camp.
Prasad, who returned here from Delhi last night, said he had told Congress general secretary and in-charge of Bihar C P Joshi of the offer.
"I have asked him to communicate acceptance before RJD Parliamentary Board meeting in Patna tomorrow at 3 PM," Prasad told reporters.
Asked to comment why the alliance between RJD and Congress was stuck, he said the offer did not mean that "everything is over" between the two parties on the issue.
"I have also told Joshi that if his party stakes claim for any other seat than he should tell me and also convince me of the winning potential of his expected candidate," he said.
To questions on whether RJD could decide to go it alone, he said, "Why are you presuming things ? ... The party's Parliamentary board will take some decisions tomorrow." Prasad said that for him and RJD the biggest challenge was to stop communal forces.
"For this we want to take all secular parties, including Congress with us." The RJD chief had said last night, "Now there will be lathbandhan (alliance of bamboo)", conveying that RJD would be taking on Congress in the poll fight.
He clarified today that he had not meant a fight with Congress, which he said, was a media interpretation.
Prasad, however, did not identify the 11 seats he has offered to Congress or the one to NCP of Sharad Pawar.
He also refused to comment on reports that RJD-Congress alliance was stuck due to conflicting claims between the two parties on Madhubani and a few other seats.
"In general the claim shall be staked on seats only on the basis of performance of the respective parties in the last general elections as per Election Commissions results."