The Blues supporters both lost their fathers after being diagnosed with Alzheimer’s.
The Prime Minister has welcomed Canadian counterpart and fellow Evertonian Mark Carney to the club’s stadium to watch a Carabao Cup tie.
Andy Burnham held a bilateral meeting with Mr Carney at Everton’s Hill Dickinson Stadium in Liverpool before the team’s third-round game with Wolves on Wednesday.
Posing for photographs in front of British and Canadian flags at the start of the meeting, in the directors’ clubroom, Mr Burnham said: “What a real, life privilege this is for me to welcome the Prime Minister of Canada.
“We share so much, Mark, we have a few Liverpool connections, Ireland connections, but, of course, Everton connections and it’s going to be a special occasion.”
He said the evening was special for a “personal reason” as there was due to be a tribute to his father Roy, who died earlier this week and had been suffering from Alzheimer’s.
His photo was shown on the stadium’s big screens before the match and was due to be shown again at half-time as a memorial.
Both leaders wore Alzheimer’s Society forget-me-not flowers on their lapels and Mr Carney said he had also lost his father to the disease.
He told Mr Burnham: “I know that struggle.”
He said the first Everton match he attended was the 1989 FA Cup semi-final, a game which Mr Burnham has also spoken about attending as it happened on the same day as the Hillsborough disaster.
Mr Carney commended Mr Burnham for his role in “bringing justice and closure” following the tragedy, in which 97 Liverpool fans died.
Mr Burnham described the former Bank of England governor as a “great progressive leader” and said there were opportunities for them to work together on defence and AI.
He said: “It’s just so good for me to think I will have somebody to talk to and commiserate about Everton at a G7 meeting.
“You are so welcome to Liverpool and obviously to your beloved club, to the new home of Everton.”
Mr Carney said there was an opportunity for the countries to “build together” in areas including values around AI.
He said: “It is an honour to be here. It is a pleasure to be here.”
After the meeting, which lasted about 45 minutes, the pair both donned blue and white Everton scarves and took their seats in the stands to watch the match.
They greeted supporters as they made their way to their seats, shaking hands and posing for photos.
Mr Burnham invited Mr Carney to watch a game together when the pair spoke in July, shortly after he became Prime Minister.
The Canadian adopted Everton as his team after moving to the UK.
Since moving into No 10 in July, lifelong Toffee Mr Burnham has continued to be a regular attendee at games at the Hill Dickinson Stadium, which opened last year.
