The concession sets the tone for negotiations over Britain's withdrawal from the European Union that are set to begin in Brussels on Monday.
The deal, however, has been met with widespread criticism from different parties amid concerns it may harm Northern Ireland's peace process.
But with the two-year countdown to Brexit already under way after Article 50 was triggered in March, he said: "We are impatiently waiting for the negotiating position of the United Kingdom gov".
Following talks in Dublin with the new Irish Prime Minister Leo Varadkar, she said that reaching a "sensible" Brexit had been the focus of their talks.
"We want to see a Brexit that works for everybody, not just in Northern Ireland from my perspective but in the Republic of Ireland as well, so it is about a sensible Brexit", Foster told reporters.
Monday's negotiations are to open at 11:00am in Brussels (0900 GMT) with 90 minutes of talks between Barnier and Davis, followed by a working lunch between the pair and a press conference.
The Queen's Speech was delayed and will now take place on Wednesday.
With an agreement between the Tories and Democratic Unionist Party (DUP) still to be reached, the British public are still none the wiser as to whether the United Kingdom is heading for a so-called "soft" or "hard" Brexit.
German Finance Minister Wolfgang Schaeuble said in a Bloomberg Television interview this week that as soon as "the principles" of Brexit are agreed, talks can move on in parallel to "the details of the regulation, and what will be the further relations between the United Kingdom, after Brexit, and the single market and the European Union, and so on".
May's plans included Britain's departure from the single market, as well as spelling out that no deal would be better than a bad deal, as far as the government was concerned.
And while Theresa May has repeatedly stated that "Brexit means Brexit", what do the two options - hard and soft - actually mean for our future relationship with the European Union (EU)?
The British public had opted to leave the European Union in a referendum a year ago, ending the country's 44-year-long membership with the bloc.
Only if "sufficient progress" is made on those thorny topics will he allow discussions to turn to the trade deal that May wants.
"And actually, getting over the fence, there might be some fresh grass out there".