The unlikely pairing has led to speculation that McCartney will soon be appearing as a guest on Corden’s celebrity singalong show Carpool Karaoke.
Corden – who has been presenting the US evening magazine programme The Late Late Show since 2015 – once described McCartney as his “dream guest” for the series.
Corden later retweeted a message from the executive producer of the show, telling fans to look out for a “star studded” Carpool Karaoke which he said would be “coming soon”.
While back in his hometown, McCartney chatted to fans, posed for pictures and shook numerous hands, before the pair jumped into a car and took a spin around the city.
Later they took a stroll along Penny Lane, the Liverpool road made famous by the 1967 Beatles song, with the 75-year-old singer signing one of the street signs along the way.
They also visited McCartney’s childhood home at 20 Forthlin Road.
McCartney later performed an intimate gig for about 50 fans, featuring both Beatles and Wings hits, at a local pub called Philharmonic Hall.