Lidington, cabinet office minister, told reporters in Glasgow that the atmosphere at talks with the Labour Party was productive.
He said he could not give an exact time for when the Brexit deal would be brought back to parliament but that it could not drift. He said the timing depended on discussions with the Labour Party.
Asked if the deal would be brought back to parliament before the EU parliament elections, Lidington said the government wanted to bring it back to parliament as soon as possible.
He ruled out any referendum on Scottish independence before 2021.