The Republic of Ireland assistant manager believes the midfielder can continue to develop at Goodison Park, despite being linked with a switch to Manchester UnitedJames McCarthy to stay at Everton amid reports linking the midfielder with a move to Manchester United.
The 23-year-old followed Roberto Martinez from Wigan Athletic to Goodison Park last summer and made 41 appearances under the Spaniard this season.
Keane, who spent 12 years at Old Trafford, insists McCarthy should opt to remain at Everton in order to continue his development.
"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."