There are also efforts to get Samajwadi Party founder Mulayam Singh Yadav to attend the rally, Ashok Singh said.
The coming together of SP and BSP leaders on one platform is being seen in political circles as emergence of a new phase of politics in the state after a dismal show by all Bharatiya Janata Party's rivals in the 2014 Lok Sabha and 2017 assembly polls.
The RJD president has also invited Mamata Banerjee of the Trinamool Congress, Naveen Patnaik of Biju Janata Dal, Sharad Pawar of Nationalist Congress Party, and many of them are likely to attend, Ashok Singh said.
The Congress is likely to be represented by its president Sonia Gandhi, Ashok Singh said, adding MK Stalin of the DMK has confirmed his participation. The effort is to repeat a Bihar-like experiment at the national level with all parties opposed to the BJP coming together, Ashok Singh said.
The coming together of sworn enemies SP and BSP in the politically crucial state of Uttar Pradesh could have a far-reaching effect to check the rise of the BJP, political analysts say. The SP and the BSP together make a formidable alliance with consolidation of Dalit and backward votes which could effectively counter the BJP, analysts say.
The BSP won only 19 seats in the assembly election this year in the 403-member house, down from 80 in 2012. This is its lowest tally since 1991, when the party won 12 seats. The SP won 47, its lowest tally since the party's inception in 1992. The SP's lowest score so far was 97 seats in 2007.
While the SP's vote share was 21.8 per cent, BSP's vote share was 22.2 per cent. BSP contested all seats while SP left 105 seats for the Congress. As the BJP's unprecedented tally dwarfed the opposition, which has together been reduced to less than 75 seats, the call for an alliance between the SP and BSP started growing louder.
BJP cornered 40 per cent of the votes polled, an increase of 25 per cent since last time, grabbing along with its National Democratic Alliance partners a whopping 325 seats.
Akhilesh Yadav has already confirmed his participation in the Patna rally. "I will be present at Lalu Prasad's Bihar rally on August 27. If there is any announcement it will me made there," he has said.
Though BSP is yet to confirm Ms Mayawati's participation in the event, its likelihood gained momentum when she attended a recent lunch hosted by Sonia Gandhi along with leaders of 16 other parties who have been traditionally hostile to each other.
Before the start of hostility between the SP and the BSP, the two parties had contested the 1993 UP assembly election in an alliance. The BSP contested on 164 seats and won 67, while the SP contested on 256 seats and won 109 in the then assembly of 425 seats, before the creation of Uttarakhand.
The government was formed with Mulayam Singh Yadav as the chief minister. The relationship, however, turned sour and the BSP withdrew support. Ms Mayawati went on to form government with the help of the BJP in 1995.
Faced with the worst political scenario with even Ms Mayawati not in a position to get re-elected to the Rajya Sabha when her present term expires in April next year, the RJD president has already announced that he was ready to send her to the Upper House of Parliament to secure her political future.