"We are trying to find a solution, it will be found through dialogue," Mahto, the president of Ajsu party, told reporters here.
He, however, did not disclose whom his five-member legislature party would vote for.
The ruling BJP has fielded S S Ahluwalia and its coalition ally Sanjeev Kumar, who had contested the countermanded March 30 elections, for the May 3 elections for two Rajya Sabha seats from the state.
Both the parties have 18 members each and depend on the same allies, including two independent candidates, to win a seat.
Pradeep Kumar Balmachu is the third candidate, and his Congress party has 13 MLAs, and banks on the support of the five-member RJD and a few small parties in the opposition.
Jharkhand Vikas Morcha (Prajatantric), which has 11 members in the assembly, has announced it would abstain from voting. PTI COR PVR