"My fear is that they will take what we've offered already and then demand some more, that's been their practice throughout the last year," Davis told the BBC 4 Radio.
The official also called the plan adopted last week "conciliatory" to the European Union.
May's plan envisions a EU-UK free trade zone for industrial and agricultural goods, as well as a common customs territory. The UK government previously was inclined to establish a full-fledged customs union regime with the bloc without any exceptions and with the application of World Trade Organization tariffs. The pullout talks are to be concluded by October, while the exit is slated for March 2019, followed by a transit period until the end of 2020.
David Davis told the BBC 4 broadcaster on Monday that Theresa May was a good prime minister, capable of surviving his resignation.
In his resignation letter, Davis cited disagreement with May's plan for exiting the European Union as the reason for stepping down.
"Yes, of course [she can survive this]," Davis said when asked whether the prime minister could survive the crisis caused by his resignation.
The former Brexit minister said he liked May and considered her "a good prime minister."Asked by BBC radio whether he wanted other ministers to follow his lead, David Davis said he did not.
"The simple truth is people can only make these decisions of conscience, decisions of principle by themselves, in their own minds," he said. "You can't make the decision for somebody else and you can't offload it on somebody else."
Davis added he would not run for the leadership of the Conservative party.
Davis resigned on Sunday after the cabinet agreed on a pullout plan that was supported by UK Prime Minister Theresa May, but not by Davis.