Graham Brady, the Conservative MP who chairs the influential 1922 Committee, is expected to table a so-called Early Day Motion criticising the government over its indecision and urging ministers to deliver a final decision by July.
The Airports Commission, led by Sir Howard Davies, first recommended building a third runway at Heathrow last July.
The government said in December that it would delay making a decision on airport expansion in the south east until at least this summer, saying "more work will be done on environmental impacts" in the interim.
"The government will undertake a package of further work and we anticipate that it will conclude over the summer," the department for transport said in a statement at the time.
When asked earlier this month, transport secretary Patrick McLoughlin refused to give MPs a specific date for a decision, saying that a pre-EU referendum purdah "may influence our ability to take a decision at a specific time" and that he would prefer not to take the decision when MPs are on holiday.
"I would like to see a decision by the time the House rises for the summer," McLoughlin said.
Brady's motion has cross-party support from Labour, SNP and DUP MPs.
The motion's full text:
"This house regrets the continuing delay in making a final decision on airport expansion in London and the South East; believes that a decision is vital for the prosperity of the nations and regions of the United Kingdom and urges Ministers to make sure that this delay is not repeated; notes that the Airports Commission spent three years and millions of taxpayers' money examining the evidence in a process that has been robust and rigorous; believes the government should get on with making a decision on airport expansion in the South East of England as swiftly as possible; further believes that every additional period of delay will cost the UK billions in lost trade and investment and damage the UK's competitiveness; therefore urges the government to use the coming months to make rapid progress and announce a final decision in parliament before the summer recess."
Commenting on the motion, Brady said the "real key" to Britain's future prosperity is "global trade with the world's most dynamic markets".
"Once the referendum is behind us ministers must prioritise a final decision about where to build a new runway and announce that decision in parliament before the summer recess.
"Every further period of delay is putting at risk the economic recovery and is a threat to our long-term prosperity."
Brady is campaigning for the UK to leave the EU.