"Jenson is a fantastic guy, a world champion and a big part of our family at Honda and McLaren for six seasons," managing director Jonathan Neale told reporters after a wet day of practise at the Japanese Grand Prix.
"We are contracted with him, we want him to stay and we like him very much," he added.
"But if your driver doesn’t really want to be in the seat, then we have to respect that."
Button's future has become a hot topic in the Formula One paddock, with mounting speculation earlier in the week that he was planning an announcement at his favourite circuit.
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Instead, the 35-year-old told reporters that they would have to wait for news.
Neale noted that had come as something of an anti-climax for the media but the team wanted to continue discussions with Button.
Former champions McLaren, in a new partnership with Honda, have had an abject season with the engine uncompetitive and unreliable and no match for dominant Mercedes.
Both Button and Spanish team mate Fernando Alonso have collected multiple penalties due to repeated engine problems and the Briton has scored just six points in 13 races.
Button spoke on Thursday about how the 'joy' of competing was missing.
"I don't think any driver has joy when they are not fighting for victories," he said. "I don't like finishing 14th, I don't like finishing 10th.
"That's not what gives me joy and excites me.
"But there are so many other things that if they work in your favour or you see a future, there's the possibility of joy coming back," added the most experienced driver on the current starting grid.
(Reporting by Alan Baldwin; Editing by Julian Linden)
