The minister said there had been some progress on issues including fishing rights as the deadline for leaving the EU looms.
He told Sky News: “I do think we’re in a reasonable position, there’s a deal to be done”.
Asked about a final deadline for talks, he said negotiations were into the “last week or so” but said the EU had previously moved the goalposts on a final deadline.
Speaking on Sophy Ridge On Sunday, Mr Raab said he would not put a percentage on the chances of a deal being struck but there had been more “respect” for the country’s position recently.
He said the UK’s position as “an independent, coastal state” meant it had to be able to control its waters but added that there could be a transition period allowing a deal to be struck over fishing rights.
He said: “We can talk about transitions and things like that and we recognise the impact on other countries round Europe.”
But Mr Raab rejected suggestions it would be enough for the EU to offer a 15-18 per cent reduction in the bloc’s fishing rights in British waters, as has been reported.
Asked about the plans to put the country into different tiers to stop the spread of Covid-19, Mr Raab said there was “light at the end of the tunnel”.
But he was unable to say the restrictions will end in nine weeks time as suggested by the Prime Minister on Saturday night.
He said: “We think by the Spring, we don’t know, but we think will be able to move to a whole different world because the vaccine will have distributed to key workers and the most vulnerable by age.”