Lesufi said they had already communicated their decision to President Cyril Ramaphosa for final approval.
He said Mosunkutu’s funeral was planned for next week, while a memorial service in his honour would be held before the end of this week.
The ANC had earlier praised Mosunkutu for the role he played in the liberation struggle.
ANC provincial spokesperson Tasneem Motara said as a trade unionist, Mosunkutu was one of the founding leaders of Cosatu.
Cope also paid tribute to Mosunkutu describing him as one of the finer leaders of his time.
Meanwhile, there has been mixed reaction on social media about the death of Mosunkutu.
Some praised him for quelling taxi violence in Gauteng as well as fighting corruption in licensing centres in the province while still the MEC.
Mosunkutu was among four MECs in November 2010 who were controversially removed from their leadership positions in government due to infighting between former premier Nomvula Mokonyane and then Gauteng ANC chairperson Paul Mashatile.
The drama played itself out at the Emerald Casino in Vanderbijlpark in October 2010, where Mashatile supporters pressurised Mokonyane to reshuffle her cabinet against her will.
They wanted the then disgraced ANC Gauteng deputy secretary, Humphrey Mmemezi, as well as former ANC Youth League Gauteng leader Lebogang Maile to be included in senior positions in the provincial cabinet.
Mokonyane bowed to pressure and showed Mosunkutu and others the door.
Eight years later, following his death on Monday this week, the controversial removal still remains in the minds of some of those who were affected by that decision.
Some took to Twitter and described Mosunkutu as a man of stature and principle, a humble servant to the people of South Africa.
“He was dumped by the greedy within the ANC led by then premier Nomvula Mokonyane. A no-nonsense public servant, Mosunkuthu was known for taking head-on the taxi violence in the province.
They further wrote: “He refused to be taken to a private hospital when a stroke hit last year but preferred public health care at Baragwanath.
“He was abandoned by his comrades since 2011 when he resigned from the legislature and had little or no help when he lost his house in Kiblerpark in a fire in 2016.”
Announcing the recall of Mosunkutu as Transport MEC on November2, 2010, the then embattled Mokonyane said: “I share the sentiment that while change can be seen as a negative thing by some, often change allows us to re-invigorate ourselves and re-look at the way we have been doing our work, especially in areas where we are lagging and where we need to consolidate our success.
“This exco reorganisation is meant to infuse our province with the requisite energy, leadership skills and experience required to ensure that we make real the promises made to the people of Gauteng when we took office,” Mokonyane said.
She added: “Mr Khabisi Mosunkutu and Ms Neliswe Moerane will be rejoining the Gauteng Provincial Legislature. I will also be responsible for the Department of Roads and Transport until the new MEC is sworn in.”
Mokonyane admitted in her media statement that she took a decision to reshuffle after consultation with the provincial leadership of the ANC.