"We can not accept a time limit to the backstop or unilateral exit clause", said Margaritis Schinas, a spokesperson for the Commission, during a regular news briefing.
European Commission president Mr Juncker said he could not rule out an extension to the Article 50 process resulting in the United Kingdom participating in the European Parliament vote.
But the European Union is adamant the other 27 member countries won't reopen the already negotiated divorce deal.
The comments came after the Prime Minister travelled to Brussels to seek legal assurances on the Northern Ireland Brexit backstop she believes are needed to secure Parliamentary approval for her Withdrawal Deal.
British MPs have voted for May to return to Brussels and negotiate alternatives to the backstop, an insurance policy in the Brexit deal created to prevent the return of a hard border between Northern Ireland and its southern neighbour.
May and the other 27 European Union leaders reached a Brexit withdrawal agreement in November but the painstakingly negotiated deal was rejected by the British parliament on January 15.
She will instead meet Juncker and Barnier, who have no mandate from Tusk's council or European Union capitals to renegotiate the deal, or to modify the infamous "Irish backstop" clause.
Now you can read the Jamaica Observer ePaper anytime, anywhere.
But Cox's legal advice that Britain could find itself trapped in the backstop indefinitely fueled fears among some eurosceptics as that would undercut a key Brexit promise of pursuing an independent global trade policy.
Ahead of May's visit, Brexit Secretary Stephen Barclay and Attorney General Geoffrey Cox travelled to Brussels to make another attempt to renegotiate the controversial Irish backstop.
But Mr Hammond said he hoped the technological solution would form part of negotiations over the following 21 months on the UK's future relationship with the EU.
The PM has promised to return to Parliament to update MPs again on 26 February and, if she had not got a new deal by then, to give them a say on the next steps in non-binding votes. Both sides have been seeking to avoid a hard border on the island of Ireland, expressing concerns that it may shatter the hard-won peace in the region.
If the U.K. Parliament does not agree on the deal before March 29, Britain risks a chaotic departure that could be costly to businesses and ordinary people on both sides of the Channel.
Another option would be for Brussels to accord Britain an extension to the 29 March deadline, which is enshrined in British law. The automaker said the decision was not directly related to Brexit, but U.K. Business Secretary Greg Clark said "decisions like Honda's this morning demonstrates starkly how much is at stake". "If such a request were to be made, no one in Europe would oppose it", Juncker told the Stuttgarter Nachrichten this week.
Jeremy Corbyn also announced he would be going to Brussels to meet the EU's chief negotiator, Michel Barnier, on Thursday.