The pair have known each other for 25 years and hugged on Friday as they met for the first time since Ms Allan gained the state's top job following the shock resignation of Daniel Andrews.
It came hours after it was revealed Victorian Labor MPs held robust discussions at a caucus meeting before selecting her to become the become the state's new leader.
Reports claim Mr Andrews remonstrated with the right faction after Public Transport Minister Ben Carroll threatened to stand for the position against the outgoing premier's preferred successor.
It would have forced a weeks-long process to select a new leader.
Mr Andrews "exploded" and swore during the meeting, interrupting Mr Carroll as he attempted to address MPs, The Age newspaper reported.
Sport Minister Steve Dimopoulos refused to reveal exactly what happened inside the meeting when pressed for details on Friday.
"Caucus meetings are generally robust and they should be," he told reporters.
He said it was not unusual that details of the meeting had leaked out but insisted the government was united.
"People have a way of moving through those discussions and getting behind the government of the day and their leaders," he added.
Mr Albanese told reporters it was good a new leader had been picked in "such a smooth way" so quickly.
Ms Allan who, like Mr Andrews, is from the left faction, was officially elected to the position unopposed less than 24 hours after his resignation.
The leadership selection could have gone on for much longer after Mr Carroll, who is from the right, threw his hat in the ring for the top job.
That would have forced a vote of party members which could have taken weeks under party rules introduced in response to tensions between former prime ministers Kevin Rudd and Julia Gillard.
Ultimately, Mr Carroll did not run for the top job and instead emerged as deputy premier, in a vote that was also unopposed.
Ms Allan is spending the AFL Grand Final long weekend finalising her cabinet and expects positions to be sorted before parliament sits on Tuesday.
Treasurer Tim Pallas will stay on in the role and Eltham MP Vicki Ward has been elevated to the ministry, filling Mr Andrews' vacant spot.
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