Mairead McGuinness has said no matter what happens between the EU and UK, there will need to be some type of agreement between them.
Ireland's EU Commissioner was speaking as chief negotiators from both sides met on Sunday at the request of Brussels and London.
European Commission President Ursula von der Leyen said on Saturday that 'significant differences remain' in several key areas.
She made the statement following a phone call Saturday with British Prime Minister Boris Johnson.
The two leaders discussed the ongoing negotiations.
In a joint statement afterwards, they said: "We welcomed the fact that progress has been achieved in many areas.
"Nevertheless, significant differences remain on three critical issues: level playing field, governance and fisheries.
"Both sides underlined that no agreement is feasible if these issues are not resolved."
Ms von der Leyen and Mr Johnson are due to speak again on Monday evening.
EU Commissioner for Financial Services, Financial Stability and Capital Markets Union Mairead McGuinness told On the Record she will be hopeful until the end.
"Even if there is no agreement, the difficulty will be that in January sometime, or in early February, the UK and the European Union are going to have to talk about things.
"Whether it's called a 'trade agreement' or whatever, there will be issues that we will need to resolve".
"So it doesn't go away: there has to be an agreement, there has to be a settlement".
'There is a good part agreed'
"It's fair to say that what is positive is that the talks continue - and until they end abruptly, I'm going to remain hopeful that there can be an agreement reached".
"There is a good part of this document agreed - what is not agreed are the sensitive issues".
But she said they can both agree on one thing.
"What I think is fair to say that both parties are keen to have an agreement, I think that's very clear.
"An I think that should be the situation given COVID - because this is adding an extra layer of trauma for businesses and people".
She said the EU's chief Brexit negotiator Michel Barnier is due to brief ambassadors early on Monday morning, "so the next 48 hours are very crucial".
Fishing 'a very big political issue'
Ms McGuinness said this process has shown that 2016 UK claims that a deal could easily be done have been put to rest.
"We now realise that when you try to unpick 37 years of cooperation, convergence, etc you're really unpicking every single aspect of how we live, work and play as neighbours."
"If you look at the politics of this and the emotion, clearly there's a great deal of political and emotional issues".
She said while fishing is not "a massive economic issue", it remains "a very big political issue".
"It's not surprising that that is there - what I think complicates the matter is none of us, wherever we are, can claim absolute territory in terms of fish and water".
"Clearly there has to be some give and take around that: you can't just exclude all EU boats from British waters entirely and forever if you want access to markets".
'Sovereign absolutism'
Ms McGuinness added that the issue of sovereignty, like any other issue, cannot be absolute and alone.
"When you live in a world with other nations, all of us are sovereign but we need to cooperate.
"What I get the sense from the UK side is that sovereignty for them is absolutism: so that if they say something that they want to do in a particular area... 'that's it and no more and they don't need to discuss it with anyone'.
"But clearly, if you look at even climate change, you can't do that on your own - you have to cooperate with others.
"So in a way I think we need to work through is why is sovereignty seen as being blinkered to the need to discuss with your former partners in the European Union to demand that it is this way and no further".
