McLaren proved more competitive this weekend and a spate of grid penalties has afforded its drivers a second row start, with Norris taking third on the grid ahead of Ricciardo.
The scenario is reminiscent of last year's running, when Ricciardo and Norris scored a sensational 1-2 for the team.
But, with McLaren's gap to the frontrunners much bigger than last year, Norris doesn't think he and his team-mate can fend off the Red Bulls of Max Verstappen and Sergio Perez, or even the Ferrari of Carlos Sainz, who is starting at the rear of the field after grid penalties.
Instead, Norris thinks McLaren is fighting for seventh and eighth on Sunday afternoon.
"Let's hope it's not too easy to overtake. I expect Max to come through quickly, Carlos as well," Norris said.
"The Mercedes [of George Russell] will probably clear off fairly quickly so, as much as I hate to say it, if we could have a seventh and eighth now then I think that's a realistic aim for tomorrow, but also a good result.
"It's quite simple, there's six cars a lot quicker than us, so we're going for that."
Mercedes' Lewis Hamilton, who starts behind Sainz in 19th after also taking a new power unit, fears cars will be unable to break out of the dreaded DRS train and joked he'd like to have his iPad in the car, so he can watch Game of Thrones while he's stuck in traffic.
When asked by Autosport about Hamilton's comments, Ricciardo thought that quicker cars would still be able to find a way through.
"Look, I don't want to go into the race being like negative about it," Ricciardo replied.
"I think last year was tough to come through the field, but I can't see it being more difficult than last year, so I think there'll be a bit more of a race on it.
"I think the quicker cars will be able to drive through and DRS trains do make it tricky, don't get me wrong, but I'd like to think there will be opportunities.
"Maybe that sort of race is good for us, you know, but I wouldn't go into the race being negative."
Commenting on what effect the difference between 2021 and 2022 cars will have on overtaking, Ricciardo added: "I think you can follow a bit closer this year but also the slipstream is not as strong, so I don't know how that kind of works itself out.
"I would be surprised if we could really hold on like we could last year because I do think you can stay closer in the second sector."
At F1's previous high-speed race, the Belgian Grand Prix a fortnight ago, the McLarens endured a torrid afternoon as poor traction out of La Source prevented them from challenging other cars on the following Kemmel straight.
Both Norris and Ricciardo finished out of the points, close to a lap down on winner Verstappen.
But team principal Andreas Seidl believes that, while McLaren's low-downforce limitations are still present, the team has found solutions at Monza that should allow it to have more of a fighting chance in traffic.
"I would say we are definitely aware of the challenge for us in the race," Seidl replied when asked by Autosport whether Spa's traction issues have been remedied.
"We have seen so far this year on low-downforce tracks, when the ambient temperatures are high as well, that we were struggling in some of the races to keep the pace up compared to Alpine for example.
"At the same time, I think we made some good changes to the car so far this weekend as well, the team did a great job to continue to improve the car.
"We will probably be in a good position to fight with all the cars around us and score points."
