The co-stars fell for one another while making the movie, and though they have been trying to keep their romance out of the spotlight, insiders claimed they have been spending a lot of time together, reported E! online.
"They got to know each other while on set. They became friends and started getting romantic a few months ago," a source said.
"They both are such great people. It's cool they got together. Everyone gets along with them. They are very well liked on set. Tom is the most down-to-earth actor."
The pair wouldn't be the first "Spider-Man" co-stars to enjoy an off-screen romance.
Kirsten Dunst and Tobey Maguire embarked on a relationship while shooting "Spider-Man" in 2002, but had split before filming the third installment in 2007.
"The Amazing Spider-Man" co-stars Andrew Garfield and Emma Stone enjoyed a three-year romance until 2015.
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