Well, almost never.
They certainly won't call you to threaten you about removing your Google listing. Which are the exact calls that business owners everywhere are getting bombarded with.
If you are running an AdWords Campaign, they may call you to help optimize that campaign. And if they are legit, they will be able to email you from an @google.com email address. If they balk at that, hang up.
And an even better rule, just hang up anyway. It's a scammer virtually every single time.
Google has finally recognized this issue and is taking steps to make the lives of business owners a bit easier.
From Google. "We’re committed to building products and programs that help small businesses grow. Unfortunately, we continue to receive complaints from business owners about calls they receive claiming to be from Google. Often these calls are actually third-party companies who are trying to take advantage of them. Sometimes these scammers claim to be able to improve a business’ Google Search rankings, other times they charge money for services that Google offers for free. Understandably, these scams are frustrating for business owners and for us at Google."
In the linked post, they go on to talk about the steps they are taking and the different business ventures they are taking legal action against.
They also mention a few tips, which I'll put below. You can read their entire post at this link.
Verify The Caller Is From Google (They aren't.)
Often these fraudulent callers will use language like, “Google specialist” or “calling about or on behalf of Google.” To verify whether a caller is actually calling from Google, you can ask that they send you an email from a Google email account to further verify their identity. Anyone who works for Google should be able to send you an email from an @google.com email account.
Claim Your GMB! (We've been telling you this for years. We also offer this service.)
Once you’ve claimed your business and actively manage your business information, you’re much less likely to be targeted by scammers.
Know What's Possible & What's Not (No. No one can guarantee you SEO results. Run.)
Know what's possible when it comes to search engine marketing. There's no way to request or pay for a better local ranking on Google. Any company that claims to be able to do so may be running a scam.
There are also links on the bottom of the page related to where you can report these callers.