It will be discussed after the drivers' briefing with the Grand Prix Drivers' Association on Friday.
Lewis Hamilton has been a powerful voice calling for change both in the motorsport industry and wider society, with F1's six-time champion launching a research commission in his own name to help increase opportunities. On the subject of taking a knee, he said: "If we are going to do it, we should all do it as a grid".
"We will do whatever we can to show that we care and respect everyone", Norris said. "We will do what is right when the time comes".
All 20 Premier League clubs have taken a knee at the kick-off of matches since England's top flight resumed a fortnight ago, in support of Black Lives Matter.
Hamilton's Mercedes team revealed on Monday that they will race with black cars in the 2020 season as part of their commitment to fighting all forms of discrimination, while also improving the diversity of their own team.
Like Hamilton, Norris will carry the "End Racism" message on his vehicle this season. "I want to do better than any other driver, but everyone should be given the same opportunity and treated the same", Norris said.
Horner added: "We also have an engine upgrade as we essentially introduce what would have been engine number two, which becomes our first engine, so in all aspects of the vehicle there has been an bad lot of work go into and it's been a race against the clock to get those updates onto the auto since reopening the factory at the beginning of June". "It's important for the safety of our Team and everyone around us in Formula One".
The new F1 campaign had been due to start in the middle of March before a member of Norris' McLaren team fell ill with coronavirus on the eve of the season opener in Melbourne.
Discussions are already under way among the drivers to choreograph a memorable show of solidarity, likely to take place just before the formation lap, in the moments when they will line up at the front of the grid for Austria's national anthem. Face masks will be a common sight in the pit lane, while every member of the travelling circus will be tested for Covid-19 before and throughout the Austrian Grand Prix. We will have people on standby and people on back-up to jump into different roles if people fall ill.