Arsene Wenger’s side face Everton fresh from a famous 2-0 victory over Bayern Munich at The Emirates in the Champions League on Tuesday night.
The north London side have won their last three games in all competitions without conceding a goal after victories over Manchester United, Watford and Bayern.
Everton, meanwhile, suffered a 3-0 defeat by the Red Devils last weekend after a stalemate with their Merseyside rivals Liverpool before the international break.
Former Toffees star Gray backed the FA Cup holders to ease past Roberto Martinez’s side despite a possible Champions League hangover.
“Arsenal will win,” Gray wrote on Paddy Power’s blog.
“Everton have to play better than last week. Howard Kendall’s passing on the morning of the United game sent Everton into a spiral of sorrow and the players never recovered.
“I expect them to be better, but I also think that Arsenal’s result in midweek might work against them and that they won’t be at full throttle.”
Arsenal can hoist themselves above Premier League leaders Manchester City with victory over Everton at The Emirates in the Premier League on Saturday.
The Gunners have collected 19 points from a possible 21 after nine Premier League games.
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