The midfielder is hoping to return this weekend having missed several weeks as a result of an injury picked up against Tottenham.
The summer signing has missed several weeks for the Blues after suffering an ankle injury in the 0-0 draw with Tottenham Hotspur at the end of August.
He has returned to fitness this week, though, and played an hour for the Under 21s in their 1-0 defeat against FC Schalke in what is sure to be a boost for him and his manager.
And he says he is hoping he can play his part against the Gunners this weekend.
“It was always the plan to get 45 minutes to an hour, so I'm pleased to come through it,” he told evertonfc.com.
"I'll see what the manager thinks, see how he feels I did tonight and hopefully I wake up in the morning, everything's fine and I'm available for Saturday if he wants to use me."
The game at the Emirates is sure to be a tough one for the Toffees, with Arsene Wenger’s side having enjoyed several promising performances over the last few weeks.
They beat Manchester United prior to the international break, before following that up with a Premier League win over Watford and a superb defeat of Bayern Munich in the Champions League in midweek.
Everton, in contrast, were poor in their 3-0 defeat to Manchester United last time out, but Cleverley expects them to bounce back positively having done so when they were beaten by Manchester City earlier in the campaign.
"We lost to Man City and we reacted to that defeat very well with some really positive results, so there's no reason why we can't do the same," he added.
"It's a tough game, they're in good form and after that there are some games that, on paper, look easier. It would be nice to really get a good result there and then hopefully string some wins together.”