The 'Baby' singer, who performed a sketch with Fey on Saturday Night Live, apparently "followed" her on set.
Showbiz Spy quotes a source as revealing: "Justin has a serious case of puppy love. He followed her around backstage like a pet labrador.
"It was obvious to the cast and crew that Justin is completely taken with Tina, and even though he is young enough to be Tina's son, she was astounded at his confidence and poise.
"Justin clearly has a thing for older women - especially Tina," the backstage insider added.
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