McCarthy is among a host of players to have been linked with a switch to Old Trafford this summer, having caught the eye with his performances for Everton during the past season.
The 23-year-old only moved to Goodison Park from Wigan Athletic last September and Keane, assistant manager for Republic of Ireland, does not see any need for him to leave.
Keane believes McCarthy is at the right place at this stage of his career and has advised the midfielder to keep performing well for Roberto Martinez's side.
"He's only been at Everton two minutes," Keane told the Irish Times.
"He's obviously making good progress but I'm pretty sure that with Manchester United there'll be talks of lots of players going there at the moment but James is at a good club in Everton.
"He's had a decent couple of seasons and if he keeps progressing then who knows but I'm sure he's happy where he is."