The BJP refused to confirm or deny the speculation but Congress insiders in Uttar Pradesh, as well as a source close to Rita, claimed it was a "matter of time" before she went over to the BJP.
Her brother Vijay Bahuguna, a former Uttarakhand chief minister who had unsuccessfully tried to overthrow the Harish Rawat government, is already with the BJP.
Rita, a Congress legislator from Lucknow Cantonment, could not be reached. Her mobile phones were both switched off and calls to her landline numbers went unanswered.
Sources said a senior Uttar Pradesh BJP leader had met Rita over the weekend to "assess" if she was keen to join the party. Based on the leader's assessment, BJP president Amit Shah is expected to take the process to its culmination.
Asked if the Congress had reached out to her, an Uttar Pradesh party source said: "No way, it's not worth it."
Rita is the daughter of Hemvati Nandan Bahuguna, a former Uttar Pradesh chief minister who spent long years in the Congress before falling out with Indira Gandhi twice, in 1976 and in 1980.
Rita was in the Congress before she left to join the Samajwadi Party that appointed her mayor of Allahabad, her hometown, in 1995.
She later returned to the Congress and went on to helm the state party.
Rita had got embroiled in a major controversy in 2009 when she urged some Dalit rape victims not to accept the Rs 1-crore compensation offered by Mayawati, who was chief minister then.
In a speech she later regretted, she had said: "Ask Mayawati if, as a victim, she would accept Rs 1 crore."
The Congress had distanced itself from the comment.
Sources said Rita was "disillusioned" with party chief Sonia Gandhi and vice-president Rahul Gandhi for announcing Sheila Dikshit as the Congress's chief ministerial candidate in Uttar Pradesh, "overlooking" her "claims".
Elections are due in the state early next year.
Rita had apparently first tapped the ruling Samajwadi Party to see if she could go back to the party on the "promise" of a berth in the legislative council. When there was no response, she tapped the BJP, sources said.
Although Rita has no mass base, BJP sources said her entry would be "symbolically" significant.
"She hails from one of the most prominent Brahmin families of Uttar Pradesh," a source said.
In the heyday of Brahmin political supremacy in Uttar Pradesh, the Bahugunas were bracketed with the clans led by Uma Shankar Dikshit (Sheila's father-in-law), Kamlapati Tripathi and Rajendra Kumari Vajpayee, said to have constituted the state's power elite.