Pirelli motorsport director Paul Hembery insists if his company were to make changes it would be for the good of the grid and not just one team.
Pirelli's tyres have some in for some criticism in recent weeks as the compounds suffer with high degradation, most notably with the soft.
As such the company opted not to take their soft tyres to Bahrain, instead giving drivers the choice between the hard and the medium.
However, according to Hembery eight of the 11 teams are in favour of Pirelli not altering their tyres.
"The reality is we are not going to do something that will suit one team," he told Autosport.
"We know what is coming up in terms of the season, and we know the results we have seen. It is not what you are seeing here, it is what is to come that we have to worry about.
"We have to take that into account otherwise we might be walking into bigger problems and then have eight teams coming to us and going: 'you do need to make a change'.
"If we do anything it will be done in the early phase of the season and then we will leave it. It is what it is then, and for better or worse you let everyone get on with it.
"You want everything you do done very early on to avoid exactly that accusation that you are influencing something. But whatever we do, we will still be maintaining a much softer tyre range than we had last year."