Showbiz
Rex Features
The pair are said to be keeping the relationship under wraps following Perry's recent split from Gym Class Heroes singer Travis McCoy.
"They've been trying to keep it very low profile," a source told Perez Hilton.
Perry was previously linked to Good Charlotte star Benji Madden, but later claimed that they were just friends.
Groban dated actress and model January Jones between 2003 and 2006.
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