It looks like things are heating up between Chris Evans and almost girlfriend Sandra Bullock. The "Captain America: The Winter Soldier" star is working hard to turn his seventh grade crush into a reality.

According to Us Weekly, the 32-year-old actor has been putting forth some real effort to woo the 49-year-old "Gravity" star. A source revealed, "Chris is pursuing Sandra." Another source added, "[Chris is] totally her type!"

An insider told E! News, "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 the two have been flying since they were spotted out together 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 Avengers" actor met the brunette beauty 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."

He added, "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."