Theresa May hopes the government’s plan, detailed recently in the Brexit White Paper, will allow the two sides to reach a deal on relations by the autumn.
Downing Street said on Sunday that cabinet ministers would be promoting the plan across Europe over the summer.
Theresa May would “take the lead” by session the Austrian chancellor, Czech prime minister and Estonian prime minister next week.
Mrs May said: “We must step up the pace of negotiations and get on to deliver a good deal that will bring greater prosperity and security to both British and European citizens.
“We both know the clock is ticking – let’s get on with it.”
Mr Raab told the BBC’s Andrew Marr Show if the “energy, ambition and pragmatism” the UK brought to negotiations was reciprocated, a bargain would be done in October.
He noted that 80% of the withdrawal agreement was already settled.
And he said it was “useful” that EU chief Brexit negotiator Michel Barnier had raised questions about the prime minister’s blueprint for the UK’s future trading relationship with the EU.
“The fact Michel Barnier is not blowing it out of the water but asking questions is a good, positive sign – that’s what we negotiate on.”
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