Steele admits he expects the former Aalesunds keeper to push David de Gea all the way for the gloves.
"The manager has got a lovely decision with Anders back, albeit with a totally disjointed pre-season, and he's got David coming back off the Olympics at whatever stage, and there is healthy competition which is what every manager wants," Steele told manutd.com.
"I think Anders has got every chance to do so [start the season as first choice]. We brought him back early, as David did on 28 June when he did two days' physical and sports conditioning and then a full week with me before he joined up with the Spanish squad. We made sure he went into there with some form of base.
"David missed pre-season last year, misses it this year and will miss it next year because it's the European Under-21 Championship again. With the value of pre-season, he's missed two and that does throw the gauntlet down to Anders.
"Of course it does and, due to the disjointed nature of pre-season, Anders has got a chance. At the Swedish, Norwegian and German games, Ben Amos will be gone by then, so we've got to travel with Anders and Sam Johnstone and that gives him a chance to say: 'Okay, I'll stake a claim'."