McLaren emerged from Bahrain's season opener as the fourth-fastest team, well behind Red Bull and Ferrari on race pace while nipping on the heels of Mercedes.
And, while it's still too early to definitively call its form compared to Mercedes, with Bahrain a tough circuit for McLaren while Mercedes suffered overheating issues, Norris believes his team will need two big steps to catch up to Ferrari and then the dominant Red Bull.
"There's a big step between us and Ferrari on a circuit like this and then another step from Ferrari to Red Bull," Norris said after finishing sixth in Bahrain.
"We've got two big steps to make up but starting with one would be good."
When asked if making those steps feels achievable this year, he replied: "To Ferrari? Yes. Again, at certain tracks, we're going to do it and, at certain tracks, we're not."
In the meantime, Norris expects Ferrari to put some pressure on Red Bull on occasion despite Max Verstappen's Bahrain dominance, pointing out Charles Leclerc's Q2 lap would have been good enough for pole.
Asked if Red Bull was on another planet, he replied: "I mean, they weren't. Carlos [Sainz] was not far behind.
"I know the Red Bull is very good on race pace and, on this track, you need to be good on tyres because it's so abrasive.
Source: Autosport