The embattled leader's message came with her government fearing a heavy defeat on Tuesday of the draft withdrawal agreement she signed with Brussels last month, AFP wrote.
Media reports said May is under pressure from her cabinet to delay the vote and fly to Brussels to secure more concessions ahead of a planned summit with 27 fellow EU leaders on Thursday and Friday.
But Brexit Secretary Stephen Barclay told the BBC: "The vote is going ahead."
May said Britain "would truly be in uncharted waters" if the draft struck after nearly two years of tough talks is voted down less than four months before the March 29 Brexit date.
"It would mean grave uncertainty for the nation with a very real risk of no Brexit," she told the Mail on Sunday.
"We have a leader of the opposition who thinks of nothing but attempting to bring about a general election, no matter what the cost to the country… I believe Jeremy Corbyn getting his hands on power is a risk we cannot afford to take."
May is facing her biggest crisis since coming to power a month after the nation voted by a 52-48 margin in June 2016 to leave the world's largest single market after 46 years.
She is under attack from more strident Brexit backers in her own party as well as europhiles who want either a second referendum or a pact that maintains stronger EU-UK ties than the one offered by May.
Her comments on Sunday are aimed at tamping down the hardline Conservative Party revolt led by the likes of her former foreign minister Boris Johnson.
May's team has been arguing for a number of days that her vision offers the cleanest break between the UK and EU that Brexit supporters can hope for at this late stage.
But Johnson used a column in the Sun on Sunday to argue that "the best way to get a great deal is to prepare for no deal" by rejecting May's draft.
Corbyn's party is hoping that failure in parliament on Tuesday will trigger a broader revolt that leads to early elections and returns Labour to power for the first time since 2010.
"I think time is really running out for her and if you can tell me if she will still be prime minister on Tuesday evening then perhaps I can tell you what we do next," Labour shadow minister John Trickett told Sky News.
"Maybe she doesn't quite know either, by the way. I think things have run out of control."
European officials said they might be able to find a way to offer a token concession in Brussels that May could take back to London and show rebellious MPs.
But they added that such tinkering cannot alter the basis of the withdrawal agreement itself.