Norris finished in P15 in FP1, and went three places better in the afternoon; finishing 12th. The F1 rookie was a place above his team-mate Carlos Sainz in FP2, but the Spaniard suffered an engine issue in the morning, a problem that kept him out for the majority of the session.
"Overall, (it's) not a bad day, not perfect and a bit messy," Norris said on McLaren's official website. "I had a lock-up in FP1 which made me lose quite a few laps and I couldn't do all the running we'd planned, but we still maximised the session and did some aero runs instead.
"We made a decent improvement between sessions and FP2 was much better, so I'm happy with what we achieved. But there's still a lot of work to do, and we need to make sure we make some more positive changes so that we can be at the front of the midfield."
McLaren technical director James Key is still hopeful his side will be able to reach Q3 on Saturday, but knows it will be "extremely tight" between the midfield.
"Good work between the sessions saw us achieve a better balance with both cars in FP2," Key said. "Lando suffered some stoppage time due to a bit of damage from kerbing.
"Getting into Q3 is likely to be extremely tight, a matter of tenths or even hundredths. We'll continue to work our way forwards."