With Ali Al Habsi on loan at Wigan Athletic and Jussi Jaaskelainen suspended, Coyle believes that Bogdan is ready to seize his opportunity, given his impressive performances in pre-season and in the previous two matches against Southampton and Birmingham.
Coyle told the club's website: "Ali had to go and get Premier League games because he had been number two to Jussi for so long.
"We always had the belief in Adam to come in and push Jussi, and that has what's happened. He played at Southampton and was terrific in the game.
"He made a big save from Cameron Jerome late on against Birmingham and that reinforced the belief we have in him.
"He has the potential to be a very good goalkeeper and we have no fears about him playing at the Emirates."