Mr Dempsey made his comments after confirming that the Government has approached the US government to introduce Customs and Border Protection (CBP) for cargo at Shannon.
The system for passengers has been operating at the mid-west airport since August last year and will be introduced at Dublin when Terminal 2 opens later this month.
Speaking in Ennis, Mr Dempsey said that if the Government could secure CBP for cargo for Shannon, he believes it would really would “hugely positive for Shannon and the region”.
The minister said he was “not minimising how difficult that might be,” but pointed out that the Americans haven’t given a blanket no to the proposal.
He said the US administration’s attitude is: “Let’s see how this (passenger CBP) works, how it goes and we will make a decision then.”
Mr Dempsey said that “now with security fears raised again, it is an opportune time over the next couple of months to raise it with them again.”
However, the minister said he could not state if or when the Government will provide funding to the proposed Lynxs cargo project for Shannon Airport.
Last year, the Shannon Airport Authority and the Lynxs Group signed a Memo of Understanding for the purpose of jointly developing a major international logistics hub and business facility at Shannon.
The agreement was seen as a significant step towards delivering a state-of-the-art international cargo facility on a 200,000sq ft site at Shannon.
The Shannon-based Atlantic Way organisation believes the development of a global freight logistics centre has the potential to create and support more than 10,000 new jobs within a five to 10-year timeframe.
However, in order for the hub to proceed, €7 million needs to be given to the Shannon Airport Authority, which has not occurred.
Mr Dempsey said: “Progress is being made. There are talks at the minute with the Dublin Airport Authority (DAA), within the DAA.
“I have been supportive of this particular project. It is back to the thing of not being as simple as some people think, that you can simply dish out money to a private company.
“There are state aid issues that arise and people have been trying to work through that, but Government is generally supportive of that particular project.
“The importance of it from a government point of view is that a facility like that might attract other similar facilities.”