The 31-year-old - a car dealer from Essex - appeared briefly on the 2016 edition of the ITV2 dating show but failed to progress into the villa.
According to The Sun, Price was set up with Woods by a mutual friend about a month ago and they have been "secretly dating" each other since.
"Katie wasn't looking for love or a serious relationship but just weeks after meeting Carl, she fell head over heels for him," a source told the newspaper.
"She's surprised how fast they clicked. He's her ideal man, really: he's got a job and his own money, he's fit, they have a laugh - and she really fancies him.
"He's told her he's not interested in being famous or another 'Mr Pricey' - he just wants to be with her."
News of Price's new relationship comes weeks after a public spat with her ex-boyfriend Kris Boyson. body check tags ::