Although stating that "no one should ever feel threatened", Ron Dennis has urged Jenson Button to "do his bit" to help McLaren move forward.
Earlier this month, Telegraph Sport reported that McLaren are considering Fernando Alonso for next season while also opening "very tentative dialogue with Lewis Hamilton."
The newspaper added that is Button's career with the Woking team that is on the line.
And although McLaren CEO Dennis has not confirmed the report, he has told Button that he needs to "try harder" against rookie team-mate Kevin Magnussen.
"I'm happy with the drivers in the sense of they are giving their best," he said in an interview with Sky Sports F1. "I'm sure Kevin is giving a big wake-up call to Jenson.
"In some ways you say 'Great, we made a great choice with Kevin'', and in other ways you say 'Come on Jenson, you are a World Champion and absolutely one thing you can do on a consistent basis - and you should be doing it - is beating your team-mate'.
"Do I want him to try harder? Of course I do.
"He is a highly paid grand prix driver, and yes we are not giving him the best car, yes it would be challenging for him to win in this car to say the least, but he could do his bit, and Kevin's got to make it as difficult for him as possible."
Asked specifically about the possibility of Hamilton returning to McLaren, with whom he won the 2008 Drivers' Championship title, Dennis went with the diplomatic answer.
"We want to win races and we will always hope that the best available drivers would wish to drive our cars," he said.
"The key word is available because people have contracts and we respect those contracts but if Lewis was in a position to drive for us next year, as many of the top drivers if they were in that position, we would love to have them on board.
"But no one should ever feel threatened, either the driver or the engineer, as all we want to do is win and we have to take considered positions and considered decisions."
Told that it 'keeps them on their toes', Dennis responded: "Absolutely."