The 20-year-old has been, arguably, the Premier League’s most impressive young player this season, and has established himself as a key member of the high-flying Toffees’ first-team.
Recent speculation has suggested that the Merseyside club are set to tie Barkley down to a new extended contract, but now City and United are keen to steal him away from their domestic rivals.
Red Devils boss David Moyes has been linked with his former player for some time, with rumours suggesting that he has been watching his development closely since moving to Old Trafford.
United could further sweeten the deal by offering Tom Cleverly – who netted in their weekend win over Aston Villa – in exchange.
But City are also interested, and have the financial clout to offer the Liverpool-born midfielder an extremely lucrative deal to make the short trip to Manchester.
However, Everton are likely to be reluctant to let their latest star move on, and may only sanction his sale if he actively seeks a transfer.