The agreement would avoid the need for an Irish backstop - which has left Britain and Brussels deadlocked - and would stop Northern Ireland being treated differently to the rest of the UK.
Ireland has hit out at reports that Britain wants the right to pull Britain out of any so-called Irish border backstop arrangement after a short period of time.
"The Irish position remains consistent and v clear that a "time-limited backstop" or a backstop that could be ended by United Kingdom unilaterally would never be agreed to by Ireland or the European Union", Coveney said on Twitter.
The hardline stance adopted by the British "stunned" Irish officials, and was viewed as a setback to clinching a Brexit deal this week.
The sides are debating how to prevent a hard border on the island of Ireland.
The Brexit figurehead was responding to reports that Prime Minister Theresa May is close to striking a deal with Brussels which would allow the creation of a whole-UK customs union, avoiding the need for the Northern Ireland border "backstop" that has been at the heart of the impasse in negotiations.
She is instead pursuing regulatory alignment with the EU and a "backstop" which would keep the entire country in the Customs Union as a "compromise" - but this would effectively preclude Britain from regaining an independent trade policy after Brexit.
There will be an "exit clause" from the customs union in a bid to convince Brexiteers that it is not a permanent arrangement as May looks to secure enough votes to get the deal through parliament, said the paper.
Asked about the report, a spokesman at May's office said: "This is all speculation".
He said: "The prime minister has been clear that we are making good progress on the future relationship and 95% of the withdrawal agreement is now settled and negotiations are ongoing".
According to the newspaper, May is also planning to reach an agreement on the EU-UK post-Brexit economic partnership, as she aspires to ensure free trade between London and Brussels.
Under the agreed deal, the European Union accepts that regulatory checks on goods can be carried out in factories and shops rather than at the border, the Sunday Times said.
Mr Coveney's spokesperson said the European Union had been united through the Brexit process and the UK had given written commitments that the Withdrawal Agreement would give a legal guarantee of no return to a hard Border in Ireland in any circumstance.
A special summit is understood to have been pencilled in for later this month to agree the final details of a deal.
He added: "We hope a deal can be done but we're not there yet".