According to the Express.co.uk report, either United or City would have to part with a world record fee of around ?100m ($13.03 million) to do a deal.
Neymar's father wants him to leave Barcelona and sees the English Premier League as his ideal destination.
Manchester United coach Jose Mourinho is said to be a long-term admirer of Neymar and now faces competition from rivals Manchester City for the wiry magician's signature.
Neymar had previously expressed his desire to play under Manchester City coach Pep Guardiola, who was also in charge of Barcelona.
"Guardiola is a guy that I really admire and who I would love to work with," Neymar, who still has four years left to run on his contract, said last year.
Neymar has so far netted 104 goals in 184 appearances for Barcelona since his arrival from Santos in 2013.
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
Doraiah Chowdary Vundavally is a Software engineer at VTech . He is the news editor of SocialNews.XYZ and Freelance writer-contributes Telugu and English Columns on Films, Politics, and Gossips. He is the primary contributor for South Cinema Section of SocialNews.XYZ. His mission is to help to develop SocialNews.XYZ into a News website that has no bias or judgement towards any.
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