Tory leadership candidate Rory Stewart says his competitors' claims they could negotiate a new Brexit deal before 31 October are "misleading".
Some candidates say they can agree a plan by the deadline set by the EU, but Mr Stewart said there was "not a hope".
Boris Johnson has warned the Tories face "potential extinction" if the UK doesn't leave by then.
Rival Jeremy Hunt said a revised deal could be done by then under a leader with "the right negotiating skills".
The former foreign secretary told a leadership hustings on Tuesday the party would "not be forgiven" if it failed, and said he was the candidate best placed to beat Labour and "put Nigel Farage back in his box".
The comments came as the Eurosceptic European Research Group (ERG) of Tory MPs called on leadership contenders to abandon Mrs May's Brexit deal and step up preparations for a no-deal exit in October.
International Development Secretary Mr Stewart told BBC Radio 5 Live's Emma Barnett that anyone promising to renegotiate by October was effectively committing to leaving without a deal because it was impossible.
Meanwhile, in other Tory leadership developments:
- In a campaign video, Foreign Secretary Jeremy Hunt says he believes that with him at the helm and "the right negotiating skills", the UK can get a revised deal with Brussels "even before the end of October." He also pledged to turn the UK economy into the "greenest in Europe".
- Andrea Leadsom told the Telegraph that as PM she would host a monthly phone-in with members of the public.
- In a statement to Bloomberg, Rory Stewart pledged to increase spending on schools, the police and research
- Sam Gyimah said the new PM should get a "final chance" to renegotiate the Brexit deal before it is put to a referendum.
- Esther McVey told LBC radio that only those who "believe in Brexit" would serve in her cabinet until the UK leaves the EU.
The EU has consistently said it is not willing to re-open the current withdrawal agreement negotiated between the bloc and Mrs May, despite it being voted down by MPs three times.
Who will replace Theresa May?
The winner of the contest to lead the Conservative Party will become the next prime minister.
Mr Stewart and Mr Johnson are two of 11 candidates running to become the next leader of the Conservative Party, and the next UK prime minister.
On Tuesday, two pulled out of the leadership race as the party tightened the rules for the contest amid concerns about the size of the field.
Candidates will now need the support of eight MPs to take part in the race, and to secure of 5% of the vote in the first round, and 10% of the vote in the second round, to progress.
Charles Walker, the acting joint-chair of the Tory backbench 1922 Committee, said it was "not unreasonable for someone seeking to be leader of the party and prime minister to be able to muster" that level of support.
He told BBC Radio 4's Today programme that he expected the Parliamentary side of the leadership contest - where MPs narrow the field down to two final candidates - to take no more than two weeks.
The winner will then be chosen by the wider membership of the Conservative Party.
Mr Johnson suggested the solution to the current deadlock would be to replace the Irish backstop - the controversial insurance policy designed to maintain an open border - with "alternative arrangements".
The EU, though, has said the backstop is a key part of the withdrawal agreement, which it is not willing to reconsider or subject to a time limit.
Mr Johnson, who has insisted the UK must leave by the end of October with or without a deal, said a no-deal exit would cause "some disruption".
But he warned that demands for a further referendum would grow if the country was forced to seek another extension from the EU.
Mr Stewart said "politicians need to stop pretending they are going to get a new deal from Brussels".
"Anyone who knows anything about Europe can assure you there is not the slightest hope of getting a new deal through Europe by 31 October. Not a hope.
"There is a lack of realism."
Earlier, Defence Secretary Penny Mordaunt would not be drawn on whether she planned to enter the leadership race, but she claimed that nobody wanted a no-deal Brexit, and the EU "understand they have to move on some things".
Speaking to BBC Radio 4's Today programme, the Brexiteer said: "I stayed in cabinet and fought to try and get a deal and to try and build a consensus, both in my party and but also in Parliament.
"What we have learnt though is if you are trying to get that objective, you can't take no deal off the table."
Fellow Leave-backer and Tory MP Steve Baker told BBC's Politics Live he had not decided whether to run, but said the party needed someone "very direct [and] with a clear plan" for Brexit.
He has published his own plan for leaving the EU, "A Clean Managed Brexit", calling for a future partnership "based not on the close mandatory alignment and single customs territory which the draft agreement was designed to facilitate, but one centred on a mutually-beneficial advanced free trade agreement".
Mr Baker added: "No one voted to ask permission to leave. We voted to leave with the hope of negotiating mutually-beneficial cooperation as an independent country. We continue to hope to do so."
What do you want to know about Brexit?
Use this form to ask your question:
If you are reading this page and can't see the form you will need to visit the mobile version of the BBC website to submit your question.