European Commission Executive Vice-President Frans Timmermans said the European Court of Justice (ECJ) will continue to play a role as the ultimate authority over disputes involving the single market.
UK Brexit minister Lord Frost has said the ECJ - which decides whether the institutions of the EU are acting legally - should be replaced with an independent arbitration panel and that it can have no role settling disagreements in Northern Ireland.
A clause in the Brexit deal called the Northern Ireland protocol has prevented a hard Irish border by keeping Northern Ireland inside the EU's single market for goods, due to its porous border with the Republic.
However, this has created a trade border between Northern Ireland and the rest of the UK, which the EU accepts is causing trading difficulties but has ruled out a renegotiation of the Protocol's text.
Tense negotiations are continuing between the UK and EU over the Northern Ireland Protocol, with the UK wanting to end the role of the ECJ in policing the agreement.
Brexit Minister Lord Frost has claimed the conditions for using Article 16 – allowing parts of the deal to be suspended – have been met because of the difficulties being caused.
Article 16 of the protocol lays out the process for taking unilateral "safeguard" measures if either the EU or UK concludes the operation of the deal is leading to serious issues.
Mr Timmermans told ITV’s Peston Show: “I think Mr Frost knows very well that this is not possible for the European Union.
“I know he knows full well that whenever the internal market is involved, the ultimate arbitrator is the European Court of Justice.
“This is, I think, extremely well-known in London and instead of talking about red lines, I think it would be more productive to talk about the ideas the European Union came up with.”
Asked about the risks of the UK triggering Article 16, Mr Timmermans added: “Let’s hope this doesn’t happen, let’s hope we can find a way out”.
He insisted Brussels had taken steps to find a compromise in the row.
Lord Frost will be in Paris on Thursday for talks with France’s Europe minister Clement Beaune.
While they are expected to discuss the row over post-Brexit fishing rights that has soured relations between the UK and France, Lord Frost is also expected to discuss the protocol.