UK and EU negotiating teams will meet later as efforts to reach a deal before a crunch summit this week continue.
After talks in Brussels this weekend, EU ambassadors were told the UK would make concessions to its post-Brexit plan for the Northern Irish border.
But the bloc's chief negotiator, Michel Barnier, said a "a big gap" remained over customs arrangements.
Home Office minister Victoria Atkins said she believed a deal could be reached by the 31 October deadline.
She told BBC Radio 4's Today programme: "[In] the last few days, we've seen a real shift in approach from the EU - and in Ireland in particular - for which we're extremely grateful and appreciative.
"I think with the negotiations ongoing... I'm an optimist, I do believe that we can get a deal by 31 October."
On Sunday, Boris Johnson told his cabinet that while he could see a "pathway" to a deal, there was "still a significant amount of work" needed to get there.
The European Commission echoed the prime minister, saying: "A lot of work remains to be done."
Both sides have said they hope to agree a deal before the EU summit on Thursday and Friday.
The government says if a plan is agreed, it will introduce a withdrawal agreement bill to be voted on next Saturday in a special Parliamentary session.
It is seen as the last chance to do this before Brexit is due to happen at 23:00 GMT on 31 October.
While efforts continue in Brussels, the Queen's Speech will take place later, outlining the government's agenda for the coming Parliament.
The government has also announced it intends to hold the Budget on 6 November, with Chancellor Sajid Javid insisting it will be "the first Budget after leaving the EU".
But Labour's shadow Commons leader, Jon Trickett, told Today he would be "surprised" if the Budget went ahead as planned as "we have no idea if they are going to get this Brexit proposal through the House or not".