The ex-defender posted an image of himself, alongside his son, also called Paul, asking his Twitter followers for any sightings.
“Has anyone seen my son Paul around Hale, Manchester, London or any airports in the past few days?” he said.
Mr McGrath, 59, said police had been informed and his family was “very concerned” about his son’s wellbeing.
He asked social media users to pass on his message and keep any eye out for the missing man.
“Please retweet,” Mr McGrath wrote.