The 17 year old is unable to sign professional terms with PSV until his 18th birthday in January, and even should he agree a deal understood to be until 2015, the Premier League trio are hopeful of landing the youngster.
Bakkali has made 12 appearances for PSV this season, scoring four goals including a hat-trick on his home professional league debut against NEC Nijmegen and has already been compared to Eden Hazard, the Belgian international.
"Zakaria is a player who scores easily, is very fast and has skilful dribbling," Belgium national team boss Marc Wilmots said.
"Zakaria has just about the same profile as Eden [Hazard]. If something happens to Eden, I will swap him [for Bakkali]."
Despite being compared to Hazard, doubts remain over Bakkali's international allegiance with the teenager still considering playing for Morocco even though he has been included in the Belgium squad for the World Cup qualifiers against Croatia and Wales.
Injury prior to the qualifier against Scotland prevented him making his international bow last month but Zakaria faces a similar dilemma which affected United midfielder Marouane Fellaini and Tottenham Hotspur's Nacer Chadli, who later both chose Belgium over Morocco.
"There are a lot of people supposedly talking on my behalf but I haven't decided yet," he told Algemeen Dagblad upon the call-up. "It's still a very difficult decision."
Players with major reputations in Eredivisie have endured contrasting fortunes upon a move to the Premier League, and Arsenal, City and United will all be sceptical over the early reviews of Bakkali's form.
PSV will be keen to sign Bakkali to a professional deal, not only to temporarily warn-off sides over making a bid for the youngster but also to increase his value ahead of his impending sale.
Dutch football is regularly used as a stepping stone to some of the biggest divisions in Europe and the likes of Arjen Robben and Ruud van Nistelrooy have successfully swapped PSV for the Premier League.
Having signed Wilfried Zaha last summer and seen Adnan Januzaj graduate to the first team this season, United are unlikely to seek another wide option, with Portuguese international Nani having recently signed a five-year deal at Old Trafford and with Antonio Valencia and Ashley Young in reserve.
City's make-up under Manuel Pellegrini has seen them neglect to field more than one genuine wide player, with Jesus Navas the primary wide option while Samir Nasri has also enjoyed success this season.
However, for Arsenal, the signing of Bakkali would suit their needs amid an injury crisis at the Emirates Stadium.
Lukas Podolski, Theo Walcott and Alex Oxlade-Chamberlain are all out injured, leaving Arsenal manager Arsene Wenger with just one genuine attacking option in Olivier Giroud.
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