The pair -- who have both been through high-profile splits this year -- were photographed in the front seat of an SUV on Saturday, in Los Angeles
In the photo, Kelly is behind the wheel and Reynolds can be seen reaching over to delicately brush away a strand of hair from her face.
A source tells ET that the pair went on a date to Cafe Stella, a French bistro in the Silverlake neighborhood of LA.
While the pair didn't show any overt PDA, their dinner outing sparked romance rumors among many fans online.
The source tells ET, "Dan is new to dating, still getting used to being single, and dealing with the aftermath of his split from Aja Volkman. His main concern is taking care of his kids and being a good dad."
The dinner with Kelly comes just over two months after Reynolds announced he and his wife, Volkman, were separating after 10 years of marriage.
"I am saddened to say that after many beautiful years together Aja and I have separated," Reynolds wrote. "Being great parents to our children is our number one priority. Thank you for always supporting us with love and care for all these years."
Reynolds and Volkman are parents to four kids -- Arrow, 10, twins Gia and Coco, 5, and Valentine, 2.