Mr Bercow has been discussing the plans while he holidays in Turkey. Sir Oliver, the former Government Policy Minister, is believed to have several potential plans on blocking the move in the pipeline. A source told The Daily Telegraph: “There are conversations taking place today.
“Letwin is seeking advice, he is around because he is speaking to officials of the House.”
Another source told the newspaper Mr Bercow and Sir Oliver “have been talking on a regular basis and I don’t find that unusual or surprising”.
The plans are reported to involve processes never used before in parliamentary history.
One involves pushing through a bill requiring Prime Minister Boris Johnson extend Article 50 by three to six months with an emergency debate potentially taking place as soon as Tuesday.
The Commons and Lords may also sit over next weekend to make up for lost days.
The last time the House sat on a Saturday was April 3 1982 due to the Falklands War.
Remainer MPs fear Mr Johnson will ask members in the House of Lords to filibuster any legislation, delaying it and throwing it out if the bills are not passed through before Parliament is suspended.
Thus peers in the upper house will attempt to pass a business motion not used in the 800 year history of Lords to place specific time limits for each stage of the bill.
Sir Oliver declined to comment when asked about his discussions with the Speaker, but is believed to have spoken to clerks in the Commons about his plans.
A spokesman for Mr Bercow insisted: “Mr Speaker has always operated an open door policy, and is happy to meet MPs from across the House representing a wide range of views.”
A Commons spokesman added: “It is common practice for Clerks to provide advice to Members on the drafting of many items of Parliamentary business, such as bills, motions and amendments.”
Other solutions being pondered by remainers include preventing Brexit supporting peers from speaking again.
The 776 member body may also be hit with motions forcing the early closure of a debate to force a vote.
Lord Speaker, Baron Fowler was a Tory before becoming speaker and renouncing party political ties.
The House of Lords is led by Tory Baroness Evans of Bowes Park.
The body is made up of 26 Church of England Bishops, 237 Tory peers, 4 DUP peers, 2 UUP peers, 178 Labour peers, 95 Liberal Democrat peers, 1 Ukip peer, 1 Green Party peer, 1 Plaid Cymru peer, 41 non-affiliated peers, 6 independents and 183 crossbenchers in addition to the Lord Speaker.
The House of Lords was historically the most powerful of the two houses of Parliament until the 19th Century, with both houses being formed in the reign of King Edward III in the 1300s, though the Lords were abolished in 1649 by Oliver Cromwell and his supporters, before being restored in 1660.