Though Button seems likely to be retained by McLaren next season the 2009 world champion still faces some uncertainty. Dennis is understood to want an 'elite' driver to join McLaren in 2015 and has ambitious plans to lure either Fernando Alonso, Sebastian Vettel or Lewis Hamilton to the team.
He does not consider Button to be in the same talent bracket as that trio, but is likely to retain the Brit if he cannot secure one of his prime targets.
Speaking with Sky, Dennis was positive about rookie Kevin Magnussen. The Dane has beaten Button on a number of occasions this season, securing a superb debut podium in Australia, but still sits 14 points behind the Brit in the world championship.
However Dennis also hinted that the team expects more of Button - not least given his significantly higher salary than Magnussen.
“I’m sure Kevin is giving a big wake-up call to Jenson,” he said.
“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 teammate’.
“Do I want him (Button) to try harder? Of course I do,” Dennis continued.
“He’s a highly paid grand prix driver, and yes, we’re not giving him the best car, but he could do his bit, and Kevin’s got to make it as difficult for him as possible.”
34-year-old Button is the second oldest driver on the grid and the most experienced with 255 grand prix starts. Should he not be retained by McLaren, his home for the past five seasons, he is expected to walk away from F1 rather than drop down the grid.