Speaking exclusively to Express.co.uk, Mr Matthews said: “The Chequers proposals, in my view, are not ideal but you know, it’s a good basis for discussion with the European Union.
“Really, the European Union needs to start engaging a bit more constructively than they have done.
“And I think if they started coming back with ideas about what they would like to see our future relationship to be, I think we’d trot to this really quite clearly and quite quickly and get a final agreement without too much trouble.
“But they are being very obstructionist at the minute and I just can’t see how it will work unless they change their attitude.”
Prime Minister Theresa May’s Brexit plan, calling for close regulatory alignment with the EU’s single market for British exports, has faced scrutiny from both Brexiteers and Remainers.
The proposal includes plans to create a ”common rule book” – involving a free trade area with the EU on industrial and agricultural goods.
The Brexit plan has been heavily criticised by former Foreign Secretary Boris Johnson since the Tory MP for Uxbridge and South Ruislip resigned over the agreement in July.
On Sunday, Boris Johnson wrote that Mrs May was wrapping a “suicide vest” around a “great British Brexit”.
But Mrs May has so far vowed to stick by her controversial Brexit blueprint.
The EU’s chief Brexit negotiator Michel Barnier has also previously rejected Mrs May’s plans and ruled out any special economic relationship with the UK – claiming it would unravel the entire “European project”.
But in a shock u-turn, Mr Barnier told a forum in Slovenia on Monday it is “realistic” to expect a divorce deal with Britain in six to eight weeks – suggesting the divorce could be settled by the week beginning October 15 – just in time for the EU Summit on October 18.
The EU chief negotiator said: “I think that if we are realistic we are able to reach an agreement on the first stage of the negotiation, which is the Brexit treaty, within 6 or 8 weeks.
“Taking into account the time necessary for the ratification process, the House of Commons on one side, the European Parliament and the Council on the other side… We must reach an agreement before the beginning of November. I think it is possible.”