Vishwas, who had unsuccessfully contested Lok Sabha polls in Amethi against Congress Vice President Rahul Gandhi, claimed that the BJP MP made the proposal at a meeting on May 19 at his Ghaziabad residence.
Though Vishwas refused to identity the BJP MP, AAP's key leader Sanjay Singh said that it was Manoj Tiwari who had made the offer.
Scotching reports about his alleged involvement, Tiwari said it was a "conspiracy" to tarnish his image by some AAP leaders.
"On May 19, a BJP MP, who happens to be a good friend, visited me along with other party leaders. During talks he made an offer that I switch to BJP and in return I would be made the Chief Minister and that the higher-ups were aware of the move.
"The BJP MP said if I agreed with his proposal he would take me to his senior leaders. I humbly declined it," Vishwas alleged.
The AAP leader's remarks came amid indications by the BJP that it was ready to take a shot at forming government in the city if invited by the Lt Governor.
The BJP rubbished the claim of Vishwas and accused the AAP leader of making baseless allegations for political gain and challenged him to provide proof to back his claim.
Strongly rubbishing the allegations, Delhi BJP Chief Satish Upadhyay said legal action was being explored against the AAP leader for making baseless allegations.
"It seems Arvind Kejriwal has written a new script for Vishwas. He should reveal the name of the BJP MP who had made the offer. This kind of baseless allegations have been made by Kejriwal in the past also and I think Vishwas is following his path," Delhi BJP Chief Satish Upadhyay said.
BJP spokesperson Sambit Patra said, "Statement of Vishwas should be looked more for entertainment value than for political value".
BJP, along with its ally Akali Dal's one MLA, had won 32 seats in the 70-member assembly in December polls. The number of BJP MLAs has come down to 28 as three party legislators Harsh Vardhan, Ramesh Bidhuri and Pervesh Verma have been elected to Lok Sabha.
With the effective strength of the Assembly being 67, BJP needs support of six more MLAs to touch the majority mark of 34.
The Congress ridiculed Vishwas' allegations saying AAP leaders were making such charges to stay politically relevant.
"The AAP usually conducts sting operation before making allegations. So if the party has any recording of the conversation, then they should make it public," said Delhi Congress chief spokesperson Mukesh Sharma.
The AAP supported Vishwas for "doing the right thing" by going public and asked BJP to drop "politics of manipulation".
"The newly elected BJP MP Manoj Tiwari had met Kumar Vishwas and offered him the post of Delhi Chief Minister. He said if you bring 18 MLAs, we will give you the CM's post," Sanjay Singh said.
But Tiwari said Vishwas has not named him and threatened to take action against any attempt to "defame" him.
"This can be a conspiracy....Maybe I have become a little dangerous for them," the MP from North-East Delhi constituency said.
AAP had won 28 seats in its debut assembly elections and had later formed the government with outside support from Congress' eight MLAs.
The government led by Arvind Kejriwal had resigned on February 14 after the party's pet project, the Janlokpal Bill, could not be passed due to opposition from BJP and Congress. President's Rule was imposed in Delhi on February 17.
The Lt Governor had not favoured dissolution of the 70-member Delhi assembly as recommended by the Council of Ministers headed by Kejriwal and kept the assembly in suspended animation.
"AAP has consistently said that BJP in its desperation to form government has been using all tricks to approach our leaders but failed. AAP has provided evidence whenever a specific news has broken out.
"Kumar Vishwas has done the right thing in going public. AAP requests BJP to drop politics of manipulation and restore democratic rights of people by joining call for elections. Let people decide," the party tweeted today.
This is not for the first time that AAP has alleged that its leaders are being poached by the BJP. Earlier also, it had accused the saffron party of approaching its MLAs for help to form the government in Delhi.