Imaginative thinking would be required to ensure trade between Northern Ireland and the Republic of Ireland was not affected, said Mr Ahern.
But he believed customs checks were inevitable.
Mr Ahern added that now was not the time for a border poll.
Speaking to the BBC's Today Programme, he said: "There has to be far more consensus, there still is a divided society, the institutions are not operational.
"The big issue, I think, for the Irish and the UK government is on the other side of 8 June is to try to help broker a deal to get the institutions back up and running and certainly having a border poll in the foreseeable future will not help that process."
In March, Mr Ahern told the BBC's Newsnight programme that dissident republicans might use the re-introduction of border posts in Northern Ireland to justify their campaign of violence.
He said a hard border with customs checks would have to be re-introduced because of the UK's decision to leave most of the customs union under Brexit.
Mr Ahern drew a comparison with the IRA's so-called Border Campaign in the 1950s.
But he said he did not expect a return to large-scale violence.
The UK government has pledged to ensure there will be no return to the "hard border" of the past.
Former Taoiseach (Irish prime minister) Bertie Ahern has warned there is no easy solution to resolving the Irish border issue before the UK leaves the EU.