Lukasz Fabianski has started Arsenal's last four Premier League games, which have all ended in victories for the Gunners.
The 27-year-old is a major doubt for this evening's match with a rib injury suffered in Saturday's 3-1 win over Norwich City.
Fabianski's knock means that countrymen Wojciech Szczesny could return to the starting XI, with Wenger insisting that he has complete confidence in both men to perform.
He told the club's official website: "Fabianski's reflexes, his positioning and his decision-making has been great. We will decide as late as possible [if he can play].
"[Szczesny has responded] really well. He worked very hard and worked very well. I do not want to make a case of it before the game. He's handling the situation very well and in a positive way.
"I have total confidence, no matter who starts the game. In the past I have shown that, that I trust these players and trust that no matter who plays, they will show their quality."
The Gunners sit third in the Premier League and are aiming for a sixth successive victory in all competitions against the Toffees at the Emirates tonight.