Significantly, the meeting took place on a day BJP's Prime Ministerial candidate Narendra Modi is here and there was speculation that Paswan would meet him.
Modi held a separate meeting with BJP chief Rajnath Singh.
The meeting came a day after LJP gave clear hints about allying with BJP after their Parliamentary Board meeting.
To a question whether LJP will tie-up with BJP, Chirag Paswan had said that "all options are now open for the LJP".
"LJP Parliamentary Board has passed a resolution that all steps, even if they are strong ones, 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", said Chirag Paswan, who heads the Parliamentary Board.
BJP leaders had also said yesterday that the talks on alliance were at an advanced stage.
Sources said the two parties are engaged in negotiations over the sharing of seats in Bihar.