The phrase "possible involvement" means that there is a chance or a likelihood that someone or something may be connected to a certain situation or event. Full definition
«You could not rule out» the Cuban government's possible involvement in the incidents, one department official said. (businessinsider.com)
«We must work to change our culture to make possible the involvement of men in the lives of their children.» (fatherhood.gov)
Speaking out during last week's Tokyo Game Show, Metal Gear creator Hideo Kojima, when questioned about possible involvement with Konami's newest Metal Gear spin - off «Survive», was adamant the espionage shooter - turned - zombie - survival game due next year has»... nothing to do with me.» (gamewatcher.com)