Tyler Cameron and Gigi Hadid's 'Dates Are Definitely Real,' Says Source: 'They're Both Being Coy'

Tyler Cameron and Gigi Hadid are two dates in, and there may be more to come.

“Their dates are definitely real and he’s having a good time,” a source tells PEOPLE about the Bachelorette runner-up, 26, and the supermodel, 24, who were spotted together Sunday night, and then confirmed to be hanging out one night later.

Still, labels shouldn’t be put on the pairing, as the source explains, “it’s too soon to say Tyler and Gigi are ‘dating.’ “

“They’re both being purposefully coy,” the source adds.

Cameron, who finished second on Hannah Brown’s recent season of The Bachelorette, was spotted with Hadid at Soho House in Brooklyn on Sunday in a photo that surfaced on Twitter.

While the photo was taken from behind, obscuring their faces, the man in the photo is wearing the same shirt Cameron was wearing in other social media posts from the same day. (Reps for both did not respond to PEOPLE’s request for comment.)

RELATED: Date No. 2? Gigi Hadid and The Bachelorette‘s Tyler Cameron Go Bowling with Friends

Just one night later, Cameron and Hadid hung out again, this time at Frames Bowling Lounge in New York City, PEOPLE confirmed. According to a source, they enjoyed a few hours of bowling in the lounge’s VIP suite with some friends, followed by an hour of karaoke.

Hadid was photographed leaving the venue in blue biker shorts, a long-sleeved shirt and sneakers.

Cameron’s first date with Hadid came two days after he was photographed leaving Brown’s Los Angeles lodgings on Friday morning. An insider told E! News they spent the night together. “I thought it went great. I think he did, too,” Brown, 24, told PEOPLE of their time together. “We had a great time. We talked everything out. It felt very normal.”

Now, the source says that “Hannah is not thrilled” about news of Cameron and Hadid’s outings.

“It’s not that she doesn’t think he’s allowed to date other people, but it’s embarrassing,” the source explains.

On Monday, Brown — who asked Cameron out during the Bachelorette finale last week after ending her engagement to winner Jed Wyatt — told PEOPLE that she’s “not really sure where things stand with [Cameron] right now.”

Brown added that for now, she has no expectations when it comes to a relationship with Cameron.

“We both have things that are going on in our lives right now separately,” she said. “I’m keeping my options open.”

She also clarified that “dating is too strong of a word” for her current situation with Cameron, and deemed herself “a single woman.”

RELATED: Chris Harrison on Why Tyler C. ‘Might Not Be the Next Bachelor’ After Being Linked to Gigi Hadid

Although Cameron seems to be enjoying his single life, it isn’t looking like he’ll be leading the next season of The Bachelor, at least according to host Chris Harrison.

“That doesn’t make him a bad guy, [but] it may not make him the best Bachelor,” Harrison told PeopleTV’s Reality Check on Monday.

However, Harrison did note several reasons as to why Cameron could make a good Bachelor, even if it doesn’t come to fruition.

“Obviously, he’s a good-looking guy,” Harrison continued. “I think you saw him, his true self when he was with Hannah and how he handled that situation. How he handled Jed, how he took care of Hannah in those situations, I think he really showed his true character, and that’s a true measure of a man, when you’re really put in those extreme situations. So he’s a good guy.”