Paul Carter said he had already talked to Kent Police and would explore possibilities with Manston's owners.
Kent MP Roger Gale said Manston's location and roads were unsuitable and the idea was "completely insane", but Manston's owners said they would help.
Stack is when lorries waiting to cross the Channel park on the M20.
It has been enforced several times in the past few weeks after striking ferry workers closed the Port of Calais.
Residents, politicians and businesses have called for alternative solutions.
Mr Carter said he would be looking into whether Manston could be used to provide temporary relief while its new owners looked for alternative uses for the site.
Mr Gale, North Thanet MP, said Manston's location was wrong because of its distance from Dover port and the Channel Tunnel.
He said east Kent MPs met the transport secretary on Monday to look at ways to resolve the problem in the long term, and he added: "I have to say that Manston was not one of the suggestions put forward by anybody."
But Ray Mallon, from Stone Hill Park, which is the new name given to the Manston site, said the owners, if asked to help by the government or Kent Police, would do so in any way they could.
He said a number of issues would need to be addressed including having consent from Thanet council, minimising disruption to local people, providing necessary facilities for drivers and ensuring safe passage of vehicles from the M20.
"Notwithstanding these challenges, we are on standby to assist," he said.
A former airport site could be used as a temporary lorry park to relieve congestion caused by Operation Stack, Kent County Council's leader has said.