The Toffees are just a single point above the drop zone at present and so far have only been able to win one top flight game under new boss Frank Lampard.
Burnley, Watford and Norwich City are three clubs currently in the danger zone, and Everton boast at least a game in hand over each of the trio.
Although the Toffees are struggling to get results to claw their way away from the relegation zone at present, former top flight star Barnes does not see them slipping down to the Championship this season.
Barnes explained that none among the current bottom three are performing well enough to guarantee finishing the season above Everton, who are capable of picking up points even though they are inconsistent on the pitch.
“I cannot see Everton being relegated from the Premier League”, Barnes told Bonus Code Bets.
“They have some inconsistency in their squad, but there are times where they play incredibly well, as they did against Manchester City.
“They can pick points up and beat any of the other teams.
“The current bottom three aren’t playing well enough to definitively say that they will finish above Everton.
“Everyone knows what football is like, it will be difficult for them.
“They must start playing well away from home and picking up points.”
Having lost three top flight games on the trot, Everton will be determined to get back into the win column on Sunday when they host Wolverhampton Wanderers.
