Premier League insiders confirmed that a meeting between the pair, brokered by its chairman Sir Dave Richards, had been agreed but not yet been scheduled.
The Premier League, which has yet to make public the size of the fine that Ferguson must pay for his refusal to speak to the BBC under new rules brought in this season, is desperate to bring a negotiated end to a feud that dates back to 2004.
Ferguson has said he will only speak to the BBC again once it has apologised. Thompson is highly unlikely to go that far, and corporation insiders hold out little hope of a settlement, though the Premier League believes there is more chance of their differences being ironed out in a face-to-face meeting.
Earlier this month the BBC contacted the Premier League to register its disappointment that Manchester United refused to speak to any broadcasters or the press after their 3-1 defeat at Anfield.
But the broadcaster stopped short of the official complaint the Premier League said was required to trigger action against the club for refusing to make a player or a member of coaching staff available to its contracted domestic rights holders, which pours £1.8bn into the coffers of clubs over three years.
The episode again highlighted the gulf between the tough league rules brought in at the beginning of the season to protect rights holders and the practical considerations in enforcing them.
The Premier League hopes to tighten rules further in the summer to require players and managers to talk to the press, as well as contracted rights holders, after every match or risk a fine. The plan will be voted on by clubs at the end of the season.
But the desire to tighten its rules further appears to jar with ongoing attempts to negotiate a truce between the BBC and Ferguson. He has not spoken to the corporation since 2004 when it aired a documentary about his son Jason, then working as an agent.
The fine against United is understood to keep ticking up every time he fails to appear in front of the BBC cameras and could now be approaching six figures. But the league is reluctant to impose it until all avenues have been exhausted and still believes a rapprochement is possible, with negotiations continuing behind the scenes.
While stressing its good working relationship with other United players and the assistant manager Mike Phelan, the BBC has consistently refused to apologise for the content of the programme – believed to be Ferguson's price for resuming relations.
Three years after the documentary was broadcast Ferguson said: "I think the BBC is the kind of company that never apologise and they never will apologise. They are arrogant beyond belief."
A BBC spokesperson said: "Our position is unchanged and we remain keen to see if there are ways to develop our relationship with Sir Alex."
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