Zak Brown is the boss of McLaren F1 and he wrote a letter to the governing body of the sport.
Penalties for Red Bull will hit the company financially and on the track.
In the current and following year's car development, any team who has overspent has an unfair advantage.
The integrity of F1 needs to be maintained, according to Brown.
The letter, which has been seen by the BBC, is dated 12 October and is addressed to the president of the sport's world governing body.
It was sent on Monday to the teams that have not committed a cost-cap offence, including McLaren.
The Red Bull team was found guilty of a "minor" violation of the cap, as well as a procedural violation.
5% of the cap is the dividing line between minor andmaterial offenses.
The details of Red Bull's wrongdoing, the negotiations that took place between the two parties before the team's final accounts were settled, or any penalties that may be handed out are yet to be given by the FIA.
The company was found to have committed a violation.
Williams was fined for an earlier procedural violation.
When asked about Brown's letter, Red Bull didn't reply. Last week, the team said they were surprised and disappointed by the decision, and that they believed the costs were under the cost cap.
McLaren didn't comment on the leak of the letter.
At last weekend's Japanese Grand Prix, Red Bull driver Max Verstappen won his second championship in a row after a close title fight with Lewis Hamilton last year.
The attempt to make it clear that Brown is expressing his views about any potential cost-cap breach is what Brown's letter does.
It does reference the crimes that were announced last week.
Brown says that policing the sport's future is critical.
If a team is found guilty of overspending, they should be hit with a double the amount by which they have exceeded the cap, as well as a reduction in their permitted research and development.
The overspend breach and possibly the procedural breeches are considered cheating by offering a significant advantage across technical, sporting and financial regulations.
An open process has been run by the FIA. In 2020 we have been given a one-year dress rehearsal with plenty of time to ask any questions. There is no reason for any team to be surprised.
The current and following year's car development has an unfair advantage to teams who have overspent.
A financial penalty alone wouldn't be a good penalty for a serious procedural or overspending violation. There is clearly a need for a sporting penalty in these situations.
It would have a significant positive and long- lasting benefit if $2m was upgraded to an annual car- development budget.
There should be a 20% reduction in wind tunnel time and a 20% overspend sporting penalty. The team has an unfair advantage that should be mitigated by these in the next year.
The process of administering the cost cap in its first season exposed the weaknesses of the rules that Brown proposes to change.
He suggests that a second minor overspend move the team to a major breech.
The 5% threshold for a minor overspend seems too large of a deviation. 2.5% is more appropriate according to us.
Brown believes that the details of the offenses should be made public.
Brown writes that it is important that the cost cap continues to be governed in a transparent way.
It will be important to know if there needs to be further clarity on certain matters after the first year of investigation. There can't be any loopholes when it comes to sharing insights or learnings.
The introduction of a budget cap has been critical to the success of F1, according to him.
The cap was part of a package of changes that were meant to make racing more competitive.
The introduction of the cost cap has been one of the main reasons we have attracted new shareholders and investors to F1 in recent years.
The rules of the cost cap are important for the integrity of F1.
It is not known if Red Bull will accept the findings of the FIA or reject them and demand to go before the cost- cap panel.
The budget cap was introduced last year and it took until October to release the findings because of the complexity of the process.