The Sun is reporting that the Premier League leaders are favourites to sign the 20-year-old attacker from New York City FC ahead of their bitter rivals Manchester United.
The same article states that Manchester City have first refusal on Harrison given their association with the Major League Soccer club despite the winger coming through the ranks alongside Marcus Rashford at Manchester United.
According to the same story, Harrison left the Red Devils at the age of 14 to move to the United States but the 20-year-old midfielder has since developed into a very promising attacker in Major League Soccer.
Harrison has scored 10 times in 54 appearances in all competitions during his two-season stint at New York City FC.
The MLS star earned his first call-up to the England Under-21 squad this month when Harrison was included in the squad to face Andorra and Scotland.
Manchester City are sitting at the top of the Premier League table but level on points with Manchester United.
The Red Devils will make the trip to their bitter rivals Liverpool in their next Premier League game on Saturday 14 October.
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