His old friend Mark Webber - who is still regularly in the paddock as a television pundit - had made the claim in Australia, amid McLaren's latest competitive crisis.
When asked about it in Shanghai, Spaniard Alonso laughed: "No, I think I'd rather be in China than home in the supermarket."
Pressed on the rumours about wanting to leave McLaren-Honda imminently, he added: "This is simply not true.
"I have read it not only in Spain but also from MotoGP riders asked if Alonso is going and everyone has their opinion. Apparently they all know that I am depressed!
"Clearly the situation is frustrating because I am better prepared than ever. But I think the team now expects extra effort from me, like in Melbourne when the simulations said that we would be last and we were fighting for 10th place.
"Forecasts for China show we are last as well so I hope it is the same as Melbourne."
Another rumour is that Alonso would support McLaren if they dumped Honda, particularly after the struggling Japanese marque recently hit back at claims about how down on power the 2017 power unit really is.
Alonso now says: "I don't know exactly how much power we lack compared to our opponents, but my feeling says 'a lot'. I notice how fast I am in the corners and how much I lose on the straights.
"As drivers we are having to work around the engine problems and we also need to save more fuel than ever before, which doesn't help."
Meanwhile, Alonso did not rule out going on the driver market later this year, amid claims that he could be lining up to re-join his old McLaren teammate Lewis Hamilton at Mercedes for 2018.
"When talking about the future, you should never exclude anything in life," he said.
"The problems I had in the past were due to the management of McLaren and never with Lewis."
McLaren finished sixth in the 2016 constructors' championship.