Puig made the comments shortly after the team announced that Marquez will not take part in today’s Dutch GP as a result of the injuries picked up in a spate of crashes last time out in Germany.
Marquez did contest yesterday’s sprint race at Assen, which he started and finished 17th following an accident with Ducati’s Enea Bastianini in qualifying.
“We have a contract, but every person is free to do what they want in life,” said Puig. “And Honda is not a company that wants to have people who are not happy being at Honda.
“So, of course we have a contract, but Honda respects Marc a lot. I want to think [he will stay] based on the contract, but I don’t have a [magic wand].”
Questioned about Puig’s latest comments, Marquez himself would not be drawn on his future plans.
“So now I am in a big moment and I cannot think about this,” said the Spaniard. “You cannot decide things about your future when you are in such a condition. During this month and a half I need to rebuild my body and the mental side.
“I am in one of the worst moments of my career. But I’m very lucky that I am in one of the best moments in my personal life, with a very good team around me. Everything is stable and this helps a lot.
“So now I need to think, to breathe, to speak with my people… and then I need to ride the bike again.
“I’ll try to start at Silverstone with the same commitment as in Portimao [the season opener]. Obviously there will be a different approach, but the same commitment.”
Marquez and Puig were both in agreement that it was the rider’s decision not to contest today’s race.
“Yesterday around eight or nine in the evening the pain really increased,” said Marquez. “I couldn’t sleep, and that’s when I decided I could not race today.
“This morning I went to the medical centre to tell them I couldn’t race. And in fact [it turns out] my rib is broken.”