Robin Thicke Is Not Secretly Married to 21-Year-Old Model Girlfriend April Love Geary: Source

Robin Thicke and his 21-year-old model girlfriend April Love Geary are currently enjoying a sun-filled getaway on Necker Island.

But while many are wondering whether the tropical vacation is actually their honeymoon, a source tells PEOPLE the two are still just dating.

The couple, who made their first public appearance together at the Cannes Film Festival last May after dating for over a year, had everyone guessing about their marital status — fueled by Instagram shots shared on Geary’s account.

They recently celebrated their two-year-anniversary with matching tattoos on their left ring fingers — her getting “RT” for his initials and he getting “ALT,” presumably for “April Love Thicke.”

“2 years strong, love you,” she wrote.

On Monday and Tuesday, Geary sparked rumors that his tattoo might be more than just a romantic gesture when she shared a cheeky photo that displayed “ALT” on her bikini bottoms.

“His,” she captioned one shot. For another, she just put a red heart.

She also shared shots smooching a shirtless, scruffy Thicke, captioning it with some lyrics from the classic song, “Sea of Love.”

“Come with me, my loveeee, to the sea, the sea of love,” she wrote.

Geary then sent out a handful of pics showing herself soaking up the sun in a leopard bikini with neon green and hot pink accents.

Though she never directly addressed speculation of their secret marriage, Geary seems to be enjoying her vacation with Thicke.

“Lucky to be in love with my best friend,” she previously said about him.

RELATED VIDEO: Paula Patton Opens up about Divorce from Robin Thicke

Thicke and ex Paula Patton divorced in March 2014. The two are parents to son Julien Fuego, 6.

Patton, 40, recently shared a vintage snap of herself and the singer in an Instagram post in August — saying she has “no regrets” about their relationship.

“Memories…I always try to only remember what was fun and made me smile,” she captioned a photo of herself and Thicke as teenagers. “My friend showed me this and it took my breath away. We were babies and we had a beautiful baby. What an amazing time in my life.”

“No regrets! Celebrating this amazing life we get to live never knowing what’s coming next,” she continued. “Love is always the answer.”