Norris dropped from ninth place to 13th and out of the points in Montreal after receiving the sanction for what the FIA deemed was unsportsmanlike behaviour.
This was in relation to what the FIA believed was a deliberate attempt during a safety car period to hold back rivals and get a buffer between himself and team-mate Oscar Piastri, who was ahead of him on track, so he did not lose time during a double stack stop.
That decision by the FIA left both Norris and the McLaren team unhappy, as they felt it had set a new precedent for behaviour during races.
Following ongoing discussions between the squad and the FIA, McLaren has now decided to take the matter further and ask the governing body to look into the situation again.
In a statement issued on Friday night, McLaren said that while it welcomed the work the FIA had done, it was not happy with its ruling on Norris. That is why it has lodged a request for a right of review over the matter.
"We are very supportive of the FIA and the Stewards, and we trust them while they carry out what is a difficult job," said McLaren.
"We appreciate Stewards need to make decisions in a short timeframe, analysing complex scenarios and often with partial information and multiple elements to consider.
"In Canada, we were surprised by the penalty and uncertain as to the rationale behind the decision. We spoke to the Stewards immediately after the race to help understand the reasoning for the penalty.
"The FIA's regulatory framework has tools and processes which allow them and the sport to deal with the operational complexity of Formula 1, especially for decisions which need to be made during the race.
"The "right of review" is one of those processes which showcases the strength of the institution in allowing decisions to be reviewed, should that be in the best interest of the sport, and this is something McLaren fully embraces and supports.
"Given this provision, the team took the initial explanation onboard and decided to review the case in a calm and considered manner, performing comprehensive due diligence, which included looking at the precedents. After this careful and extensive review, we believe enough evidence exists to a submit a "right to review" to the FIA, which we have done so.
"We will now continue to work with the FIA closely, in the same constructive and collaborative manner in which we normally do and will accept the outcome of their deliberations and decision."
For a request for a right of review to be accepted, teams need to supply a new element that was not available to the FIA at the time the decision was made.
The FIA's International Sporting Code states that if: "a significant and relevant new element is discovered which was unavailable to the parties seeking the review at the time of the decision concerned, the stewards who have given a ruling or, failing this, those designated by the FIA, may decide to re-examine their decision following a petition for review."
The FIA has said that a hearing in to the matter will be held on Sunday morning, ahead of the Austrian Grand Prix. The first issue to decide will be whether or not McLaren's fresh evidence is a "significant" new element.