The Brazil international is currently on loan at Bayern Munich, and the Bundesliga champions have the option to sign him on a permanent deal at the end of the 2019-20 campaign.
Bayern are allegedly unlikely to take up the £102m option, though, which has led to suggestions that Barca would be prepared to sell Coutinho for between £68m and £77m this summer.
According to The Express, United and City are both monitoring developments ahead of potential bids, although Chelsea, Tottenham Hotspur and Liverpool are also considering summer approaches.
The 27-year-old has scored 21 times in 76 appearances for Barca since arriving from Liverpool in January 2018 for a fee that could eventually reach £142m.
This season, the South American has contributed seven goals and eight assists in 26 appearances for Bayern, including one strike in six Champions League outings.