If he does so, it is understood he would be the first Leader of the Opposition to refuse to be sworn in the presence of the monarch. Orders in Council are usually used only for Privy Council members who are based abroad, such as prime ministers of Commonwealth realms.
'Deeply insulting'
One member of the Council was appalled at the snub, saying: "Firstly it is deeply insulting and secondly it is not grown up - not to go to see the monarch is just extraordinary.
"I am sure that what they would have done is not make him kneel. But what this really means is that he is not prepared to put himself in the position of a serious leader who can be trusted."
The Queen, who returned to London from her summer holiday in Balmoral on Wednesday, will meet her Privy Councillors for the first time in 10 weeks on Thursday at Buckingham Palace, and might reasonably have expected Mr Corbyn to take the opportunity to be sworn, a process which gives him the right to receive government intelligence briefings.
One Whitehall source said: "The whole point is that he is entering into an agreement with the State which gives him access to material and creates a relationship of trust.
"If he were to go down the route of becoming a member through an Order in Council that would probably be an indication that he never intended to attend.
"He is under no obligation to attend in person but any leader of the Opposition would normally be expected to be there."
'Prior engagements'
Mr Corbyn was invited by David Cameron to join the Privy Council when he phoned him to congratulate him on becoming Leader of Her Majesty's Most Loyal Opposition, to use his full title, after he was chosen by the Labour Party on September 12.
It was then up to his staff to contact Buckingham Palace and confirm the date when he will attend to be sworn. Buckingham Palace does not issue a formal invitation.
Mr Corbyn's spokesman said the Labour leader was invited to attend Thursday's meeting but had sent his apologies, citing "prior engagements". A source close to Mr Corbyn insisted: "It's not a snub."
He declined to say when he might attend a meeting of the Council, saying: "That needs to be resolved. I don't know what his timetable is."
The Privy Council, whose origins date back to Norman times, has more than 600 members, including government ministers, bishops and judges, but only a handful usually attend its monthly meetings.
Mr Corbyn's predecessors Ed Miliband and Gordon Brown were already members of the Privy Council when they became Labour leader, having previously been Cabinet ministers, while Tony Blair was sworn in six days after becoming Labour leader. David Cameron was sworn just over a week after becoming Tory leader, and his immediate predecessors were already members through previous front bench experience.
Michael Foot, Labour's most left-wing leader of recent decades before Mr Corbyn, was already a member when he led the party, and Neil Kinnock was sworn just over two weeks after he was elected leader.
Typically a leader of the opposition will only attend one meeting of the Privy Council, but Mr Corbyn has questioned whether the Leader of the Opposition should have to join the Council at all.
Asked last month if he would kneel in the ceremony, he told the BBC: "'I didn't know that was involved actually. So we'll have to find out about it, OK?"
Perpetual rebel
Sir Alan Duncan, a Conservative MP and a Council member, said: "'The Queen has always put herself above politics, but Jeremy Corbyn seems to want to put his politics above the Queen.
"This is not so much about snubs, insults or ceremonies: it's more about whether Jeremy Corbyn wants to be a serious political figure or just a perpetual rebel."
Tory MP Keith Simpson, a member since last year, said: "It is a snub for the Queen in the sense that she is a constitutional Monarch and she represents the constitutional way in which we do business."
"Either he has got a more important engagement - I can't think what, or I suspect he is trying to delay the moment.
"Once you are sworn in as a Privy Councillor then you can be told certain things in confidence and as far as the Leader of the Opposition is told you are told things that are serious.
"If you are not sworn in, you can't be told. It may be that he does not want to be constrained by being told things that involve national security."
The Cabinet Office, which speaks on behalf of the Privy Council, and Buckingham Palace both declined to comment.
The news came as Tony Blair said it would be inappropriate to talk about Mr Corbyn during a visit to the 9/11 memorial and refused to mention the new Labour leader by name.
In response to a question about whether he welcomed Mr Corbyn's election Mr Blair said he would not answer, "particularly not here in this museum memorial to 9/11."
Mr Corbyn has described the killing of Al Qaeda mastermind Osama Bin Laden as a "tragedy".
