D Dipasupil/Getty; Dimitrios Kambouris/Getty
After the former Alaska governor and vice presidential hopeful, 57, was seen at an Upper East Side restaurant this week in Manhattan with the retired New York Rangers player, speculation sparked about a new romance.
The pair was photographed at Elio's eatery on Wednesday evening, and Page Six reported on Friday that they have been an item since late last year.
However, a Palin source tells PEOPLE they're "just friends" who "met through hockey." (Duguay could not be reached for comment.)
Duguay, 64, was married to supermodel Kim Alexis from 1993 until 2013.
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Palin was in New York ahead of a trial for a libel lawsuit she brought against The New York Times. The start of that trial was pushed back by a federal judge after he learned Palin was again infected with COVID-19. (Jury selection is now set to begin Feb. 3.)
"By repeatedly flouting CDC guidelines, Ms. Palin has shown a complete disregard for the health and safety of small business workers and her fellow patrons," Adams' spokesman Jonah Allon said in a statement.
"The city offers multiple resources to support isolation for those who test positive for COVID-19, and we encourage Ms. Palin to join the 98 percent of New Yorkers who report they have followed guidance on isolation and have helped New York City stop the spread."
This is apparently the second time Palin has been diagnosed with COVID, after she announced an earlier infection last year. But that hasn't stopped her from visiting New York City restaurants right before and after being tested.
According to the Times, Palin also ate indoors at Elio's in Manhattan last Saturday. The restaurant said it made a mistake allowing her to eat there because it requires guests to provide proof of vaccination to eat indoors, and Palin is not vaccinated.
D Dipasupil/Getty Sarah Palin
She was back at Elio's on Wednesday after her positive test results were revealed, the Upper East Side eatery's manager said.
"In accordance with the vaccine mandate and to protect our staff, we seated her outdoors," Luca Guaitolini told the website Gothamist. "We are a restaurant open to the public, and we treat civilians the same."
"We encourage any New Yorker who came into contact with Sarah Palin to get tested, just as we encourage all New Yorkers to get tested regularly, especially those who believe they may have been exposed to COVID-19," the mayor's spokesman previously told PEOPLE.
* Reporting by ADAM CARLSON