McLaren team principal Martin Whitmarsh is pinning some of the blame for Lewis Hamilton's string of clashes with Felipe Massa on Jenson Button's form.
Hamilton and Massa collided again during Sunday's Indian Grand Prix while Button finished second behind winner Sebastian Vettel.
"Lewis, the great, exciting driver that he is, will not like being beaten by Jenson," said Whitmarsh. "For any driver, the first driver you want to beat is your team-mate."
Hamilton, the 2008 world champion, came home seventh in India after his chances of a podium finish were ruined by a crash while trying to pass Massa on lap 24.
Massa was adjudged to be in the wrong, receiving a drive-through penalty before retiring later in the race after hitting a kerb and damaging the front suspension on his Ferrari.
Button, meanwhile, finished second behind world champion Vettel to consolidate his second place in the championship, 38 points ahead of fellow Briton Hamilton.
Button, the 2009 world champion, has recorded three wins and been on the podium 10 times this season. Hamilton has scored two victories of his own but also picked up six penalties.
Whitmarsh added: "Lewis will be feeling under pressure because of the great performances from Jenson at the moment. I don't want him to enjoy being beaten by his team-mate. I want him to try to beat Jenson, just as I want Jenson to try to beat Lewis."
Whitmarsh rejected suggestions he and Ferrari should organise a meeting to clear the air: "They're men, they've got to figure it out for themselves."