Massachusetts would be making a mistake if it just proposes one site for Amazon as the online behemoth looks for someplace to put its second headquarters, Gov. Charlie Baker said Wednesday.

"I think the best thing we can do with respect to Amazon is to give them what I would describe as a menu of options," Baker said.

Massachusetts is a "big time player" in biotechnology, health care, artificial intelligence and robotics, according to the governor.

Amazon says the second headquarters could bring a $5 billion investment in the region and up to 50,000 high-paying jobs.

"I think the best thing we can do is say, 'Massachusetts has a ton of capabilities that should be important to you and we're making a series of investments in areas that should matter to you as well,'" Baker, who expects more than a dozen proposals across the state, told reporters outside his office on Tuesday.

"I think picking one site would be a huge mistake," he continued. "'Cause if you pick one site what you're basically saying is it's here or nowhere.

"I think we should be fans of every proposal and our job is to basically make the case that Massachusetts is the best place for them to be," Baker said.

A number of cities and regions, including Boston, are expected to submit bids, which are due to Amazon by Oct. 19.

Worcester officials have also discussed a bid, while the Economic Development Council of Western Massachusetts said it backs siting the second headquarters in Enfield, Connecticut.

If Massachusetts makes it to the next round, state officials will get a better sense of what the company wants, and the list of sites is likely to narrow.