"My party is building up and we are growing from strength to strength. I have no plan to merge my party with SP. It is too late in the day. However, if there is a proposal for an alliance, we may consider the same," he said.
Akhilesh, on the other hand, is said to be completely against the return of his estranged uncle to the SP fold.
"With great effort, Akhilesh has managed to establish himself as the undisputed leader of his party and he naturally does not want his uncle to return and challenge his authority again," said a supporter of the SP chief.
Mulayam, who initiated a patch-up effort between his son and brother after the BSP called off its alliance with the SP, has warned the family that unless it unites, its political survival would be at stake.
Three members of the Yadav family -- Dimple Yadav, Dharmendra Yadav and Akshay Yadav -- have lost the lok Sabha elections and the party's tally rests at five members in the Lok Sabha.
Akhilesh, too, is facing pressure from his cadres. Having failed in the 2014 Lok Sabha, 2017 Assembly and now 2019 Lok Sabha elections, his leadership is now being questioned and if he fails to put his act together, the voices of dissent may grow louder.
The relationship between the uncle and nephew has deteriorated so much that recently when both visited the ailing SP patriarch at his Lucknow residence, when Chief Minister Yogi Adityanath also happened to be there, the two failed to exchange even a word.
Shivpal said he was open to alliances in the upcoming bypolls to 12 Assembly seats. Of the vacant seats, 10 belong to the BJP and one each to the SP and BSP.
Mulayam, despite his poor health, is said to be in constant touch with Akhilesh and Shivpal and is persuading them to forgo their differences in the larger interest of the family and the party.
It was on Mulayam's insistence that the SP did not moved a petition seeking Shivpal's disqualification from the membership of the state Assembly even though he has formed his own party.
A senior leader close to Mulayam said "Unless the SP unites, the future seems uncertain for all. Akhilesh has failed on the issue of alliance -- 2017 with Congress and 2019 with the BSP. Shivpal, too, has not made much of an impact with his new party. It is Mulayam's earnest wish to unite the two and he will continue in his efforts."