Co-chairmen Sir Jim Ratcliffe and Joel Glazer, football board member Sir Dave Brailsford and sporting director Dan Ashworth were in attendance, in addition to INEOS sport chief executive Jean-Claude Blanc, and Ten Hag's position as manager is thought to have been one of the subjects discussed in Knightsbridge.
Man United have made their worst-ever start to a Premier League season, picking up eight points from their first seven matches to sit down in 14th spot in the table.
However, as it stands, Ten Hag remains in charge, with the Dutchman soon set to begin preparing his side for the Premier League contest with Brentford next weekend.
According to The Independent, during the meeting on Tuesday, one Man United chief put forward the argument for Ten Hag to be sacked immediately, but others argued that a change at this stage would be disruptive.
One Man United chief 'called for Ten Hag to be sacked'
The report claims that there are also concerns over the suitability of the managers being mentioned as potential replacements for Ten Hag.
Ruud van Nistelrooy, who is currently the assistant manager at Man United, continues to be linked with the role on an interim basis, while Thomas Tuchel and Graham Potter are also seemingly in the frame.
However, Gareth Southgate, who left his role with England after Euro 2024, has ruled himself out of the immediate running, with the former Three Lions head coach not planning to return to coaching for at least another 12 months.
Ten Hag came close to losing his job earlier this year, but the FA Cup final win over Manchester City is believed to have convinced Man United chiefs to keep him in the role for at least the start of this season.
The Red Devils are again struggling, though, and the club's former captain Roy Keane has hit out at the current state of affairs, claiming that he 'no longer recognises the club'.
Keane slams Man United for current state of affairs
"I don't know (on whether Ten Hag will last until the end of the year). I'm sure club's have board meetings all the time, I'm sure they're constantly discussing the manager, recruitment and staff," Keane told Sky Sports News.
"But to me, United was always about good people and good characters, and people who could play for Man United, and deal with it, but I don't see that now. I don't recognise this team, I don't recognise the club.
"A couple of months ago everyone was saying, 'they've got new people coming on board, they'll have all the answers', more money on recruitment and United have gone backwards.
"They're chopping and changing and getting rid of everyone in the background which is fine, there's a business side to it, we know that. But when we're discussing Man United it's more like a business than a football club. Football clubs are about people and good people who turn up and put a shift in and who are good, honest people.
"We all work in sport and in different environments and it's about working with good people, and what I see at Man United, stepping back a bit, and it might be a bit harsh, I'm not sure I'm seeing proper footballing people who are making the right decisions for the club."
Man United will be bidding to record just their fourth win of the season in all competitions when they welcome Thomas Frank's Brentford side to Old Trafford on October 19.