The 20-year-old, who joined the Hoops on an 18-month deal in January of 2016, has been a key member of Brendan Rodgers' side this season and has contributed with 13 goals in all competitions.
The Sun quotes a City source as saying: "Celtic have shown an interest in taking Patrick back again and are willing to pay a big loan fee for him.
"He has been there 18-months already and has been a star. He is very highly-rated both sides of the border.
"Pep would like to take a closer look at him to see if he is ready to play for the club on a regular basis next season though."