While they may not be officially boyfriend and girlfriend it looks like Chris Evans and Sandra Bullock could be in the early stages of dating.

It seems, the two stars are getting to know each other as they share a mutual attraction to one another.

According to E! News, a source revealed "They are not in a relationship, but they are definitely hanging out and are in the early getting-to-know-each-other phase," adding, "They haven't put a title on it, but they really like each other."

Romance rumors for they two have been flying since they were spotted out in early May after they grabbed a bite to eat with Chelsea Handler at Cecconi's in West Hollywood.

Just a month before that, Evans and Bullock dined at West Hollywood restaurant Craig's with Handler and Melissa McCarthy.

The "Captain America: The Winter Soldier" actor, 32, met the "Gravity" star, 49, at the Vanity Fair Oscar party back in February 2012.

Three months later Chris Evans told Playboy, "I used to be in love with Sandra Bullock when I was growing up. Sandy B. was my girl," adding, "I remember seeing Speed when I was in seventh grade and just thinking, 'That's her.'"

That same year, the actor told Details magazine that he had a "big poster" of Bullock when he was younger.

At the time the actor was single but he later got back with his on again off again girlfriend Minka Kelly, whom he started dating in 2007.

Meanwhile, Bullock, has maintained her single relationship status since her 2010 divorce from Jesse James.

That same year Evans described to Women's Health what he looks for in a girlfriend.

He explained, "I like women who get emotional about babies and puppies. I've met some incredibly cool women who are tough, but the woman you marry should have a really soft side."

He also revealed that he despises "arrogance and false modesty" in relationships. "The Avengers" actor explained, "Nothing is worse than a beautiful girl fishing for compliments by saying how gross she is."

He added, "On the flip side, I find genuine humility and modesty attractive."

Chris Evans told Playboy, "I like girls who are self-deprecating. I like girls who make fun of themselves. If you can't poke fun at yourself, what are you? I just want someone with a good soul. That's about it," adding, "The rest I'm really flexible on."