The council has agreed to investigate the costs of holding such training courses and also to contact neighbouring parish councils to see if they would get involved.
It followed a motion by Councillor Jay Moore who said at a meeting at the Guildhall on Wednesday he had been contacted by Oswestry man, Darren Fraser.
"Defibrilators across Oswestry have had the specialised bleed kits installed," Councillor Moore said.
"But Darren has pointed out that we really need to give training in the use of these bleed kits."
Councillor John Pryce said this training would have to be a rolling programme to ensure that people were trained regularly.
The meeting agreed to a suggestion by Councillor Les McGuire to look to involve parish councils as well.
Clerk, Arren Roberts, said the council would need to investigate the costs involved. He said it may be that a trial training event could be put on and the public invited to take part.