Garff MHK Martyn Perkins said the public are "sick of dog mess dirtying the streets and popular walks".
A two-week consultation will be launched by the Department of Environment, Food and Agriculture to gauge public opinion.
Currently, owners can be given a fixed penalty fine of Â£50 or taken to court if they don't clean up after their dog.
The proposed system will see swabs taken from dogs' mouths and compared to samples taken from faeces.
Mr Perkins said he had "already had lots of feedback from responsible owners who support the move", adding: "It is certainly a case of the minority ruining it for the majority."
He said the issue needs to be dealt with partially because the island's "outstanding natural landscapes" have recently been recognised by UNESCO.
"We are very proud of this status and we want to encourage people to take pride in their environment," he said.
If it is supported, DNA testing could be included in a bill, currently going through Tynwald, which aims to amend the Dogs Act 1990.
The bill would mean every dog on the island must be implanted with a microchip, which would see an end to the licensing and duty regime for dogs.
Microchipping became a legal requirement in the UK in 2016.
DNA testing of dog poo has been backed by a Manx politician who wants it used to tackle fouling on the Isle of Man.