The 25-year-old singer and the 20-year-old model recently decided to take their relationship to the next level after being friends for several years and things between them are heating up fast.
A source said: ''They're inseparable right now. Things have gotten serious pretty quickly.''
The duo were first linked last September while the blonde beauty was on a break from her on/off boyfriend Cody Simpson, 18, but she split from the Australian singer for good in May.
However, friends are concerned Joe is too mature for Gigi.
The insider explained to US OK! magazine: ''Joe's only five years older than Gigi, but he's had at least a decade more in the Hollywood spotlight. Gigi's friends are happy for her, but they're worried that if she can't keep up, he'll ditch her.''
Joe has been supporting the Sports Illustrated model as she looks after her ill mother, Yolanda Foster - who is suffering from Lyme disease.
A source previously said: ''Gigi's main focus right now is looking out for her mom, Yolanda.
''Everything with Joe happened so quickly, she didn't expect it, but she doesn't want to get too carried away just yet and wants to make sure she spends time with her mom, helping her out as much as she can.''