This meeting would grant Capello "access to the immense knowledge'' of individuals such as Arsène Wenger, Sir Alex Ferguson and Roy Hodgson, according to the LMA chief executive Richard Bevan.
The FA on Thursday night acknowledged the receipt of the letter which was "in the system'' awaiting action.
The FA stressed that Englandmanager Capello – or his assistant Franco Baldini – was already in communication with managers. Yet a more formal, potentially fruitful interchange is now on offer.
"Capello is a highly respected manager, well liked by the managers,'' said Bevan. "We want to work closely with England.
"There were mistakes made in the World Cup but the feedback I've had from members is 'how do we help the England manager?'
"In the Nineties, managers used to come together and advise the FA. We can help Fabio by ensuring he has the access to a think-tank. These guys know what they are doing.
"One manager said to me that if England want to win a World Cup or European Championship they had to have a club mentality.
"To play with a club mentality the England manager has to understand how a club player ticks, therefore you have to work very closely with the club managers. I want to encourage that.
"I am certain the FA and Fabio will come along to a dinner every couple of months and debate players, football and strategy and issues.''
One of the issues the LMA think-tank will address is how best to nurture Capello's successor. "The next manager should be English if at all possible,'' continued Bevan.
"There are 63 of the 92 league managers [who are] English but what are the FA doing? They should be identifying talent and deciding who are going to be the likely pool [of England managerial contenders] in two years, five years, 10 years, 20.
"If the FA genuinely want an English England manager, they can't just sit back and wait. They have to be proactive. They have to invest. That's why we are massively excited by the National Football Centre. It will help prepare coaches.''
Prepare them for the rigours of what LMA think-tank men like Wenger have endured. When Bevan asked Wenger how managers survive, the Arsenal manager answered with a moral. "A world-famous pianist was playing at a concert,'' Wenger said.
"A good piano player went to the concert to listen to the 'master'. After the performance he was so excited because he has the opportunity to meet the 'master', his idol. He says to the 'master'. 'To play like you, I would give my life.' The 'master' replied: 'I have'.''
Wenger himself embodies that doctrine of utter dedication.
Such qualities will suffuse the managers invited on the think-tank, high-profile men like Wenger, Ferguson, Hodgson and David Moyes as well as those in the Football League.
"That think-tank will meet on a regular basis, not just about England and the FA but to debate other major issues our members think very strongly about like refereeing, goal-line technology, the NFC, the 2018 bid, and showing more support for the FA Cup.
"On refereeing, the fourth official is now able to advise a referee if a key incident has been missed and potentially that is a great risk to managers.
"We'll have a think-tank on that with managers from every league, and senior people, and perhaps Mike Riley of the Professional Game Match Officials Ltd (PGMOL) joining us.
"The FA should have come along to the LMA and say we need to improve refereeing, we need to look at goal-line technology, what do you think about the 25-man squad? They would get back collective views of very experienced people.
"There is not enough communication between the various stakeholders of the game for the betterment of the game.
"We have a unique position that we have 250 members with 95,000 matches of experience with unbelievable amount of knowledge and passion for the game.
"With all respect to the FA, they haven't managed. They miss things that are obvious to technical people. The Government have embraced the think-tank and will be at the first think-tank dinner on Nov 4.''
Other issues up for debate by the think-tank include the transfer window, governance, club ownership, the 25-man squad ruling, doping regulations, youth development, betting, agents regulations and a mid-season break.
"We are being proactive. We are doing an in-depth study into the technical area here and in other countries to see if we can do it better.
Should it be where it is or, like rugby, where the coach sits in the stand or in the Gods?'' TV likes confrontation between managers on the touchline.
"It might do but is that good for the LMA and its members? We are also trying to work with Sport England to get out-of-work managers to mentor young athletes, swimmers and gymnasts for 2012.''
Oh God brb dying........especially from Postman Capello and Arsene Cera up there..