The minutes should be released "to clear up any confusion and avoid accusations of hypocrisy", says the shadow culture secretary.
Ed Woodward reportedly did not discuss the Super League during the meeting
Labour has urged Downing Street to release details of a meeting with Manchester United's executive vice-chairman a few days before the European Super League announcement.
It is understood the prime minister was not in the meeting with Ed Woodward and that the controversial competition was not discussed..
Mr Woodward talked about COVID restrictions and "the return of fans to stadiums" with Number 10 chief of staff Dan Rosenfield, according to club sources quoted by The Independent.
It reports that Mr Woodward was introduced to Boris Johnson after the meeting.
Manchester United fans were among many angered by the breakaway league
Labour shadow culture secretary Jo Stevens said minutes of Wednesday's meeting should be released "to clear up any confusion and avoid accusations of hypocrisy".
She added: "The prime minister and his ministers made very public and vocal condemnation of the European Super League. The public would therefore expect the same message to have been delivered in any private meetings."
The league's announcement caused uproar at the weekend when six Premier League clubs said they were joining some of Europe's elite teams in the fenced-off competition.
Boris Johnson was among the first to criticise the proposals and vowed to do all he could to stop it.
The league was roundly criticised as a money-making exercise and against the spirit of the game due to the lack of relegation and promotion. The backlash led the Premier League teams into a swift U-turn and the project now appears all but dead.
On Tuesday, shortly before Manchester United confirmed their withdrawal, Mr Woodward said he would be stepping down from his position. Sky Sports News understands it was because he could not support the owners' plans.
The club's American chairman, Joel Glazer apologised "unreservedly" to fans on Wednesday and admitted they had "got it wrong".
A review of the way English football is run has also been announced in the wake of the controversy.
It will consider setting up a new regulator, changing the "fit and proper test" for owners, and look into how fans could have more of a say.
Former sports minister Tracey Crouch will be in charge and it's hoped it could be a "watershed moment".
The "50 + 1" model used in Germany's Bundesliga will be examined, in which fans must own the majority of their club, meaning commercial owners cannot push through unpopular profit-driven changes.
The review will also look at issues such as whether the criteria to test the suitability of owners and directors should be added to, and if the oversight of clubs in foreign hands is sufficient.
Ms Crouch said: "Football means so much to so many people in this country and my review will be firmly focused on the fans.
"It will look closely at the issues of governance, ownership and finance and take the necessary steps to retain the game's integrity, competitiveness and, most importantly, the bond that clubs have with its supporters and the local community."
The review will be presented to current sports minister Nigel Huddleston, Culture Secretary Oliver Dowden, and the Football Association, before being set out in parliament.
Source: Sky News