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.
So far more than 33,000 have retweeted Mr McGrath's message, with many users offering words of support.
“Hope he turns up safe...every parent’s worst nightmare losing their kids,” wrote one who gave his name as John H.
Another tweeted: “Now you were a proper player lad. I hope your son is found safe and well Paul.”
Meanwhile, a number of users shared sightings of young man they thought could be Mr McGrath’s son.
Two reported seeing a boy that matched Paul’s description in the centre of Northampton, while another person thought they saw him at the Aldgate tube station in London.
A Manchester Police spokeswoman confirmed a "missing person case" had been opened, but she said no further details were available.
Mr McGrath has been contacted for further comment.
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