The former justice and housing minister served as chief of staff to Mr Davis when he was shadow Home Secretary from 2006 to 2010.
Mr Raab supported the Leave campaign in the 2016 EU referendum and sat on the committee that set strategy for the official Vote Leave campaign.
In 2016, Mr Raab suggested the former UK ambassador to the EU, Sir Ivan Rogers, was "scarred" by "pessimism" in response to claims that the UK might not strike its own trade deals until the mid-2020s.
“He was the diplomat who persuaded David Cameron to dilute his ambitions for the renegotiation, which was one reason the referendum was lost," Mr Raab said.
"So, he has been rather scarred, in fairness, by his own pessimistic advice in the past.
“But, I think it’s reasonable to set out the very worst case scenario for a five to 10-year period to iron out all the details of a trade deal.
“I respect the Foreign Office’s professionalism, but they have always been very pro-EU, and very anti-leaving the EU.
“Let’s not be consumed by Sir Ivan’s gloomy pessimism, let’s get behind the Government, let’s set out the case for a strong, post-Brexit relationship with the EU on trade, security, and other areas."