"Replacing me is not going to make the (Brexit) negotiations any easier and it won't change the parliamentary arithmetic", she added.
Meanwhile, Labour's Jeremy Corbyn, also speaking on Sky News, touted the possibility of a general election and claimed a second Brexit referendum was "an option for the future".
According to excerpts from May's speech, cited by Reuters, EU nationals "will no longer be able to jump the queue after Brexit" noting that the United Kingdom system will be focused on business and "will have more streamlined application and entry processes".
Sir Graham also told the BBC's Sunday Politics North West it was "very likely" Mrs May would win a vote of no-confidence if there was one.
But May told the Sky News programme "Ridge on Sunday" that there are not now enough letters to threaten her premiership, and even warned rebels that a new contest risks the entire Brexit process.
Britain's former Brexit minister Dominic Raab said on Sunday that Prime Minister Theresa May's Brexit deal was fatally flawed but she could still change course, Reuters reported. If 48 (15% of) Conservative MPs write such letters to the chair of the 1922 Committee, it means the party has lost faith in May's leadership and a new leadership contest must be triggered.
The casualties for May included her second Brexit secretary to quit the job, Dominic Raab, after she and her counterparts in the European Union came to an agreement on a 585-page hard fought deal that included a demand from the EU's chief negotiator, Michel Barnier, that the texts needed to be made public as soon as the deal was announced.
"He thinks what I am doing is important for the British people, though he doesn't put it like that.
It goes alongside the future relationship", she said.
Suspenden concierto de Inti Illimani por grave accidente del staff
El vehículo chocó en el kilómetro 82 de la Ruta 5 Sur, la madrugada de este domingo , específicamente en el Bypass Rancagua. Inti Illimani suspendió el concierto que tenía este domingo luego de conocer el fatal accidente que los afectó directamente.
Two Cabinet ministers and several junior Government members quit, and more than 20 politicians have submitted letters of no confidence in Mrs May.
Mrs May defended last week's draft agreement for leaving the European Union and said there was a "critical" week ahead.
The UK will remain part of crucial European policing and security arrangements until December 2020, including EU databases of missing people, arrests, DNA, fingerprints and vehicle number plates.
She is due to say: "It will no longer be the case that European Union nationals, regardless of the skills or experience they have to offer, can jump the queue ahead of engineers from Sydney or software developers from Delhi".
She is due to say that she expects to hammer out a framework for a future trade relationship in Brussels this week, before signing off the deal at a summit on Sunday.
She said of her week: "It's been a pretty heavy couple of days", admitting to the Mail that when she went up to her Downing Street living area late on Wednesday the first thing her husband Philip did was to pour her a whisky.
"I think there's still the potential to improve on the clarification and on some of the measures within it and that's what I'm hoping to be able to help with", she said.