"If there is no breakthrough in the coming week, the balance of opinion in parliament is clear -- that it would be better to seek to... delay our date of departure rather than crash out of the European Union on March 29," the ministers wrote in the Daily Mail newspaper.
They added: "Beyond the next few days, there simply will not be time to agree on a deal and complete all the necessary legislation before March 29."
But they warned that leaving the EU with no deal would "severely" damage the economy, weaken national security and risk the break-up of the UK.
May was in Brussels this week for talks with European Commission president Jean-Claude Juncker and will meet European Council president Donald Tusk on Sunday at an EU-Arab League summit in Egypt.
She has promised to update parliament on her efforts on Tuesday and either put the new deal to a fresh vote of MPs or allow them on Wednesday to debate their own ideas for the way forward.
One of these is expected to be a plan to delay Brexit to avoid a "no deal" scenario.
The ministers warned their hardline Brexit-supporting colleagues who continue to oppose May's Brexit deal that MPs will not allow Britain to leave the EU with no deal by default.
"If that happens, they (the eurosceptics) will have no-one to blame but themselves for delaying Brexit," they said.
Business minister Greg Clark, work and pensions minister Amber Rudd and justice minister David Gauke wrote an article stating their opposition to leaving the European Union on March 29 with no deal.