Irish prime minister Leo Varadkar said an arrangement with a time limit would not be "worth the paper it's written on".
The border issue is the main barrier to progress between the two sides.
With time running out, Theresa May, who briefs her cabinet on Tuesday, has to get both the EU and her MPs on side.
The UK is due to leave the EU in March, and although 95% of the deal is said to be complete, the tricky bit is proving to be how to honour the commitment by both sides to guarantee no new hard border in Ireland.
It is an issue because after Brexit it will become the UK's land border with the rest of the EU, which has a single market and customs union so products do not need to be checked when they pass between member states.
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