John McDonnell said he is willing to work with Tony Blair to heal divisions within Labour.
The shadow chancellor has already offered to meet arch-critic Lord Peter Mandelson for a cup of tea and he has now extended that invite to Labour's former prime minister.
Meanwhile, Mr McDonnell insisted Jeremy Corbyn will lead Labour into the 2020 general election as he said possible leadership successors needed to gain "more experience".
He also categorically ruled himself out of a future run for the leadership.
Mr McDonnell, one of Mr Corbyn's closest allies, hit out at Mr Blair and Lord Mandelson in the run up to the Copeland and Stoke by-elections after the pair made high-profile interventions.
Mr Mandelson said he was working "every single day" to bring Mr Corbyn's leadership to an end and Mr McDonnell claimed a "soft coup" to oust the leader was under way.
When asked on The Andrew Marr Show on BBC One who was leading the coup, Mr McDonnell said there were a "number of people" within the party who were "stirring" ahead of the two by-elections.
Mr McDonnell said: "There must have been people on the end of that line and the end of that email chain to receive it.
"Actually, what is interesting, as I say, I think we have all looked over the edge on Copeland and we have decided we need to unite the party now and yes, I will be having a cup of tea with Peter Mandelson.
"There will be lots of things we agree upon. There will be some disagreements. But I think the most important thing that we have got is a responsibility to our party but more importantly to the country."
When asked if he would also be willing to have a cup of tea with Mr Blair, he said: "Of course. I am willing to talk to anybody. We need advice from everybody."
Mr McDonnell was also asked about a push to change Labour rules to make it easier for a left wing candidate to make it onto the ballot paper in a future leadership election.
He said: "Let's get this clear. I want to be absolutely clear: John McDonnell will not stand for the Labour leadership ever in the future again, full stop. I have made that clear time and time again."
He continued: "Jeremy Corbyn will lead us into the next election.
"Of course we are building up a succession for the long term future and we have got some really great young talent coming through but they need more experience before eventually they will succeed."