Juncker told the lawmakers that "we are not throwing the British out".
East Antrim representative Sammy Wilson has expressed regret for his choice of language when referencing the Irish premier's stance on Brexit.
Both ministers said the Treasury's Project Fear campaign, which warned Britain's economy would immediately tank if we voted Leave, has now been proved wrong. However, May's spokesman said on Tuesday that there was no question of not following through in March next year on the referendum vote of June 2016 to leave the EU.
In an interview with the BBC yesterday, McGuinness reiterated a call for mutual market access for European Union and United Kingdom financial services, and today told Reuters a deal was "absolutely possible" though she said Britain "will get less than what we have at the moment whatever the settlement".
Responding to the PM's comments, arch-Brexiteer Jacob Rees-Mogg urged her to back her words - and back Brexit publicly.
British Prime Minister Theresa May, who campaigned against Brexit in 2016, has insisted that she will see it through, despite a flurry of statements this week by European Union leaders that they would welcome Britain changing its mind.
Just last week the new Tory Party chairman Brandon Lewis - a former Remain campaigner - said he would now vote Brexit to "respect the first referendum". He said he did not have any reaction to Mr Wilson's comment about the Taoiseach.
Mrs May also revealed that she travel to the Munich Security Conference in February, where she said Britain would reaffirm their commitment to "European defence and security".
Earlier in the same interview Mrs May was asked "do you feel European".
"If tomorrow, or the day after, the United Kingdom made a decision to change its mind, it's clear that we would look at this with kindness", the adviser said.
'It's in many ways her misfortune to have Brexit looming large over everything because, much as she's committed to delivering it, it's not something that animates her or she would have chosen to be her legacy'.
"I would have thought she would want to advocate that loudly and I would urge her to do so".
Some observers were quick to point out that Ireland's wartime government under then Prime Minister Eamon De Valera maintained a position of at least formal neutrality.