Marquez secured his fourth premier class title in five years this season, and has only competed for the works Honda team since making his MotoGP debut in 2013.
But his close links to Red Bull have prompted speculation that he could switch to KTM at some point in the future, as the energy drinks giant is the Austrian firm's title sponsor.
Marquez, along with the vast majority of the MotoGP grid, is out of contract at the end of the 2018 season, but Alzamora said Marquez is keen to stay at Honda for the foreseeable future.
"Marc never forgets that Honda was the manufacturer that gave him the opportunity to make his debut, to win races and MotoGP titles," Alzamora told Spanish newspaper El Periodico.
"Honda will always be Marc's first choice."
Marc Marquez (Honda Repsol) lors des essais de fin de saison à Valence
Image credit: Getty Images
Honda is keen not to repeat the mistake it made with Valentino Rossi in the early 2000s, when it underestimated the Italian's role in its success and eventually lost him to rival manufacturer Yamaha.
Ex-team principal Livio Suppo believes Honda would be willing to step up its financial commitment to ward off potential interest from rival factories.
"Marc is the best rider, he's irreplaceable," Suppo told Autosport before his departure from HRC.
"He's the rider everyone would choose to have, and that's why we really appreciate having him.
"Re-signing him will depend on whether he has a willingness to win for another manufacturer and also on his feelings with next year's bike. But, financially, I don't think Honda will have a problem in making him a good offer."
Marquez's last contract renewal was announced in June 2016, and was worth close to £8million a year.
But given Jorge Lorenzo is now earning closer to £12m at Ducati, it seems likely Honda will have to improve its offer to a similar level to be certain of retaining its number one rider.