The Blues boss's contract is up in the summer, and Holloway thinks that the Scot might allow his contract to expire and decide to end his 11-year association with the club.
"Moyesy looks like he will become the first Premier League manager ever to allow his contract to expire," Holloway wrote in his column in The Mirror.
"Only David himself knows what his plans are for the future. But I am a believer that managers can overstay their welcome.
"Everton are a great club and David Moyes is a great manager. You would think they are made for each other. But sometimes, not even the greatest love affairs last forever."
Everton beat Manchester City 2-0 in the Premier League yesterday.