The DUP believes Mrs May is prepared to give into Brussels" demands and agree a "backstop', which would see Northern Ireland treated differently from the rest of the United Kingdom after Brexit and effectively create a new border in the Irish Sea.
Meanwhile, in a leaked letter, Theresa May's hinted there could be customs checks in the Irish Sea in the event of no-deal with Brussels.
May's letter to the DUP said that she "could not accept there being any circumstances or conditions" for the Northern Ireland-only backstop coming into effect.
However, in a post on Twitter, Ms Foster wrote: "The PM's letter raises alarm bells for those who value the integrity of our precious union and for those who want a proper Brexit for the whole UK".
Theresa May's Brexit plans have come under fresh doubt after her Democratic Unionist party allies (DUP) said a letter from her "raises alarm bells", suggesting she will not be able to depend on its support to get the proposals through parliament.
If May can clinch a deal with the European Union, she still needs to get that deal approved by parliament.
Lidington was speaking after the DUP's Brexit spokesman, Sammy Wilson, warned that his party was prepared to vote against May's deal.
"From what we can see in the letter which has been sent to Arlene and Nigel (Dodds), it is quite clear some of the promises made do not conform to some of the content of the letter".
Man Killed In California Mass Shooting Survived 2017 Las Vegas Massacre
There's a fence right there so I said: "'Everyone get over the fence as quickly as you can.' And I followed them over". The officer was on the phone to his wife when the emergency call came in, telling her: "Hey I gotta go handle a call.
Prime Minister May already has a challenge on her hands in getting a Brexit Withdrawal Agreement through Westminster this winter with a majority of Labour MPs and some Conservatives set to vote against it.
At issue is the vexing problem of how to avoid border checks between British Northern Ireland and the Republic of Ireland after Brexit enters into force on March 29.
Britain's culture minister Jeremy Wright arrives In Downing Street.
He said the two sides were discussing how to avoid a hard border between Ireland and Northern Ireland. It can not be watered down or bargained off.
"A successful outcome is not guaranteed but I think it is possible in the next couple of weeks", Varadkar said at the British Irish council on Friday.
Scottish First Minister Nicola Sturgeon was among the leaders at the Isle of Man summit and urged Tory leaders to consider keeping the whole of the United Kingdom in the single market, warning that Brexit has highlighted "real weaknesses" in the UK's devolution settlement.
A potential sticking point could be demands for European Union fishing fleets to be given continued access to British coastal waters as the price for agreeing to Mrs May's UK-wide backstop, the Daily Telegraph reported.
May will meet Belgian Prime Minister Charles Michel this morning before heading to France where she will meet President Emmanuel Macron, who is one of EU's the most hardline leaders when it comes to Brexit.