BJP sources said an alliance with LJP could swing between four to five percent votes and help the combination raise its tally substantially in Bihar where 40 Lok Sabha seats are at stake.
"The talks have reached an advanced stage," a source said.
The sources dismissed reports that BJP will give eight seats to LJP, saying that is too many.
Asked about the benefits of such an alliance, the sources said, "When one percent of swing can decide the government in Chhattisgarh, a swing of four to five percent of votes can be crucial in the three-cornered contest in Bihar."
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They also discounted the fears of many state leaders, who had a meeting with party president Rajnath Singh yesterday, that an alliance with LJP may be detrimental to BJP.
The sources said BJP would ask LJP not to field leaders with criminal background in case of an alliance.
BJP spokesperson Shahnawaz Hussain, meanwhile, claimed that there was no offer yet from Ram Vilas Paswan.
"We want to have an alliance with 121 cr people of India. Whosoever offers us help to make (Narendra) Modi the PM, we welcome them," he said when asked about party's position on possible alliance with LJP.
BJP also hit out at CBI over reports that it may question Paswan in a corruption case, saying the probe agency is a "loyal Congress ally" which becomes active whenever a UPA ally appears to be heading for a split.
"CBI is generous to those who shouts slogans in the support of Congress and harass those who do not do so," Hussain said.