Scottish Prime Minister Nicola Sturgeon has said that "there is no good reason" for Scotland not to obtain a similar Brexit agreement with Northern Ireland.
It has been suggested that the United Kingdom might be willing to accept that NI will effectively remain in the EU single market after Brexit.
The talks between the leaders of the United Kingdom and the EU have not yet led to an agreement.
Theresa May said that "the differences" said she was "sure" that an agreement could be reached.
Amid speculation that Northern Ireland could receive special treatment, Ms. Sturgeon questioned why other parts of the United Kingdom should not do so, a position endorsed by the mayor of Sadiq Khan and the Welsh prime minister, Carwyn Jones.
Khan said that such a measure would have "great ramifications", while Jones said that different parts of the United Kingdom could not be treated "more favorably" than others.
- The United Kingdom and the EU fail to reach an agreement on the Brexit negotiations  Kuenssberg: Brexit and Ireland, and now what?
Mrs. May will meet with the President of the European Commission, Jean-Claude Juncker, and the President of the European Council, Donald Tusk, with the hope of reaching an agreement on the first phase of Brexit. summit within ten days.
There have been reports that Northern Ireland could maintain a "regulatory alignment" with the EU, although the final wording of any possible agreement has not yet been confirmed.
Belgian MEP Philippe Lamberts told the BBC The political editor Laura Kuenssberg said the UK had made a concession on the Irish border, saying the ministers were willing to accept that Northern Ireland remain in the single market and the customs union in everything but name. However, Downing Street sources have probed caution, suggesting that there are "parts still moving" about the deal.
If a part of the UK can maintain regulatory alignment with the EU and effectively stay in the single market (which is the right solution for Northern Ireland) surely there is no good practical reason why others can not.
– Nicola Sturgeon (@NicolaSturgeon) December 4, 2017
Ms. Sturgeon posted on Twitter : "If a part of the UK can maintain regulatory alignment with the EU and effectively stay in the single market (which is the right solution for Northern Ireland), surely there is no good practical reason why others can not. "
Referring to Norway's membership of the EU single market, added : "If it is not some kind of Norwegian status" for the entire United Kingdom, it must mean some kind of special treatment for NEITHER. It has to be one or the other. And if the latter, why not also for Scotland, London and Wales (if you want)? "
Mr. Khan said that there could be" great ramifications for London "if Ms. May" admitted that it is possible for part of the United Kingdom to remain in the single market and in the customs union. "
Mr. Jones said: "We can not allow different parts of the UK to receive more favorable treatment than others.
"If a part of the United Kingdom is granted, the continued participation in the single market and customs union, then we expect to receive the same offer".
Ms. Sturgeon has argued for a long time that Scotland could remain in the single market while the rest of the United Kingdom leaves.  The government's Brexit document, published in December 2016, argued that Scotland could remain in the single market through the European Free Trade Association (EFTA) and the European Economic Area (EEA).
But Secretary Brexit David Davis rejected the idea, saying there were "clear barriers" wh This could create "additional controls and controls on trade within the United Kingdom."
He stressed that the UK government wanted to achieve "the freest and most frictionless trade with the EU" while "maintaining the commercial and economic relationship deeply integrated with the EU".
But he said that "any divergence between EU legislation and the United Kingdom" could lead to "new trade barriers within our union" and "a significant disruption of the domestic market". He added that "companies could face a confusing mix of regulatory regimes."
DUP leader Arlene Foster said her party "will not accept any form of regulatory divergence" that separates Northern Ireland from the rest of the United Kingdom.