In Touch Weekly have alleged that Hamm, who is in a longtime relationship with actress/director, Jennifer Westfeldt, is secretly dating Moss after they had been spotted alongside each other several times over the last few weeks.
Representatives for 43-year-old Hamm and 31-year-old Moss have vehemently denied that there is any wrong-doing being conducted, and they insist that the pair are "just friends."
However, recent witnesses to their outings have claimed that the pair were inseparable together - and they even visited Disneyland as a twosome over Easter.
"I saw them at Disneyland on Easter," said a fellow visitor to the park. "It was just the two of them. They were walking around the park, trying to be incognito."
This was then followed by the recent unveiling of photographs that showed the pair at a New York Starbucks together on April 23. Reportedly both Moss and Hamm tried to remain unseen and wore long coats, hats and sunglasses to hide their identities.
TheFrisky.com also reported after these photos of the twosome enjoying an espresso together emerged that because they looked as though they were "trying to hide their identities... they must be having a secret affair." However, the comment was firmly tongue-in-cheek.
Hamm has been dating Westfeldt since 1997, and he has previously insisted that despite the fact that they aren't legally married their relationship is just as intimate as couples that are.
"We may not have a piece of paper that says we're husband and wife, but after 10 years, Jennifer is more than just a girlfriend," he declared. "What we have is much deeper and we both know that. To me, people [should] get married when they're ready to have kids, which I'm not ruling out." The duo even own their own production company, Points West Pictures, too.
Meanwhile, Moss was previously married to Saturday Night Live's Fred Armisen, however their marriage disintegrated after less than a year, and they officially divorced in May 2011.
In 2012 she commented on her ex-husband, "One of the greatest things I heard someone say about him is, 'He's so great at doing impersonations. But the greatest impersonation he does is that of a normal person.' To me, that sums it up."
[Image via Joe Seer/Shutterstock]