Mr Burnham said firefighters’ training and pay would need to be looked at if they took on this “extra responsibility”.
But he said the union had indicated it would support the plan.
He told Radio Manchester he did not know the cost of the proposal yet, but promised to consult with residents as it could lead to changes in council tax.
There are 41 fire stations across Greater Manchester spread across the region’s 10 districts.
The average response time of crews was seven minutes 30 seconds, Mr Burnham said, meaning they were “faster” than ambulances.
“That’s no criticism, but through getting defibrillators more quickly to people who need them in Greater Manchester, we will save lives.
“It’s the right thing to do,” he said.
The move would help free up the North West Ambulance Service in times of “increased pressure and demand”, the mayor added.
Mr Russel said the proposal would be developed in collaboration with “staff, trade unions, and our partners” to build on the pilot and provide the “best possible service”.
The North West Ambulance Service has been contacted for comment.
