Collins and Efron were first rumoured to be dating earlier this month, when they reportedly left a Los Angeles steakhouse together after sharing a meal.
The stars were spotted getting cozy again at a birthday party for a mutual friend at an LA eatery on Saturday (February 4), according to People.
An eyewitness told the website: "They even walked in holding hands… [Efron and Collins] had a drink at the bar together and then joined the birthday crew on the patio."
Representatives for Efron and Collins haven't commented on the report.
Efron famously dated his High School Musical co-star Vanessa Hudgens, but they ended their relationship in December 2010.
The actor recently sent well-wishes to Demi Moore following her hospitalisation for exhaustion last month.
Efron stars in The Lorax, which is released in the US on March 2 and July 27 in the UK.
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Watch a trailer for The Lorax below: