"There are certain economic sanctions that we can take which are being considered right now," Ghobash said in the interview, which was published on Wednesday.
"One possibility would be to impose conditions on our own trading partners and say: you want to work with us then you have got to make a commercial choice," he added.
The four countries have not provided any evidence for their claim, while Qatar has repeatedly rejected the allegation.
Ghobash said that if Qatar "was not willing to accept the demands, it is a case of 'Goodbye Qatar' we do not need you in our tent any more".
'We don't claim to have press freedom'
On Thursday, the Saudi-led bloc issued a 13-point demand list in exchange for the end of the anti-Qatar measures and gave a 10-day deadline.
The demands included, among others, that Qatar shut down the Al Jazeera media network, close a Turkish military base and scale down ties with Iran.
When asked if the closure of Al Jazeera was a valid demand, Ghobash told The Guardian that the UAE does not "claim to have press freedom".
"We do not promote the idea of press freedom. What we talk about is responsibility in speech," he said.
He added that speech in the Gulf "has particular context, and that context can go from peaceful to violent in no time simply because of the words that are spoken".
Ghobash also said that the UAE was willing to hold itself to the same standards it was asking of Qatar.
He echoed previous statements by UAE officials that the Gulf states do not wish to escalate the conflict with military action.
"We can escalate with more information, because we are not going to escalate militarily. That is not the way we are looking at things."
Source: Al Jazeera and news agencies