Sources in BJP said on the condition of anonymity that there have been talks between Joshi, daughter of former Chief Minister late Hemwati Nandan Bahuguna, and its leaders. A decision on her joining the party can be taken soon, they said.
67-year-old Bahuguna, currently an MLA from Lucknow Cantonment, could not be reached for her comments on the reports.
Bahuguna is said to be unhappy with the Congress leadership over projection of Sheila Dikshit as the party's chief ministerial face and feels increasingly marginalised since Raj Babbar was made the UP party chief.
She believes she had better credentials to be projected as a Brahmin chief ministerial face than Dikshit. She also faces a tough electoral prospect as Congress candidate in the coming state elections.
Bahuguna's brother and former Uttarakhand Chief Minister Vijay Bahuguna had joined the BJP a few months back.
Her joining the BJP will be a shot in its arm as it will help the saffron party consolidate Brahmin votes, eyeing which the Congress had declared Diskhit as its chief ministerial pick.
At the AICC briefing, Congress spokesperson Manish Tewari said some television channels have been running this with a question mark but party spokespersons do not answer speculation.
"We would not respond to any kind of speculation," he said.
The speculation was triggered by reports that Bahuguna had a meeting with a BJP leader, said to be party chief Amit Shah, recently.
"She has not denied it (meeting with Amit Shah)," a senior Congress leader said on condition of anonymity.
He said Bahuguna, who is also Congress spokesperson, is unwell and is convalesing in New Delhi.
Congress leader Dwijendra Tewari when contacted said he was sure that she will take a decision which will be in the interest of the party and the situation will be clear soon.
Congress is already facing a steady flow of its MLAs to rival camps before the 2017 Assembly polls and this could be a major blow to the party.