The sources said talks have also been on with actor-turned-politician Jaya Prada and a decision on her joining the party is yet to be taken. Sources close to Ms Jaya Prada - who has been in the Samajwadi Party and the Telugu Desam Party before - is ready to join the BJP.
All Thursday morning, there has been speculation that the party could consider fielding Ms Bedi or Ms Jaya Prada against Aam Aadmi Party president Arvind Kejriwal in his New Delhi constituency for the assembly elections next month.
BJP sources said though Ms Ilmi is expected to join the party, she is said to be reluctant to contest the elections, especially against her former boss, Mr Kejriwal.
BJP chief Amit Shah is scheduled to address a press conference this evening, heightening the expectation that he could announce the entry of Ms Bedi and even Ms Ilmi into the party.
Kiran Bedi, who has not confirmed or denied that she will take a plunge into politics, tweeted this morning, "Delhi and Delhites do not deserve this kind of prolonged negativity. The Capital needs integrity wisdom, experience, vision and implementation"
Delhi and Delhites do not deserve this kind of prolonged negativity. The Capital needs integrity wisdom,experience,vision and implementation-- Kiran Bedi (@thekiranbedi) January 15, 2015
Ms Bedi was a prominent member of what was called Team Anna, a core group of activists who worked closely with Gandhian activist Anna Hazare when he launched his campaign to demand a bill to appoint a Lokpal or national ombudsman against graft.
Mr Kejriwal too was a member of Team Anna, but he later fell out with Mr Hazare over his decision to launch a political party. Ms Bedi has since been a stern critic of Mr Kejriwal.
Days after Prime Minister Narendra Modi led the BJP to a massive victory in the national elections last year, Ms Bedi had signalled her readiness to join the party. "Narendra Modi's call to the nation inspired me. My earlier aversion to politics has declined considerably," she had told NDTV.