The LJP, according to sources, initially sought that 10 Lok Sabha constituencies should be allocated to it to contest for in Bihar, and wants at least eight constituencies now.
The party Wednesday said it is looking for "alternate allies" and the option for BJP is open.
"...all steps..., should be taken in the interest of the party and if an alternative alliance is to be firmed up, party chief Ram Vilas Paswan should take the decision," LJP leader Chirag Paswan said after a meeting of the party's parliamentary board.
LJP chief Ram Vilas Paswan, Chirag's father, admitted there were strains in ties with Lalu Prasad's Rashtriya Janata Dal (RJD) and that the talks for an alliance with the Congress did not show much progress.
He added: "There is a deadlock in our alliance with RJD, all options are now open, including a tie-up with BJP."
He added that a final decision will be taken in next three to four days.
The Paswan community, over which the LJP has considerable influence, accounts for anywhere between four to five percent of voters in the state.
The LJP was part of the Congress-led United Progressive Alliance from 2004 to 2009 with Ram Vilas Paswan being a cabinet minister. The party lent outside support to the UPA II.
Paswan left the BJP-led National Democratic Alliance and resigned from the Atal Bihari Vajpayee government in the wake of Gujarat riots in 2002.