The 'Jealous' singer and 'Quantico' star sparked rumours of a relationship two months ago, and have since travelled the world, including meeting each other's families at weddings.
Revealing the couple could be ready to take the next step, a source told E! News: ''Priyanka and Nick are still very serious. They have a very healthy relationship and truly are a good pair.
''Nick has basically been living in Priyanka's New York City apartment with her and they spend a lot of time together. They next step is him permanently moving in, and it has been a discussion.''
The famous pair recently spent the 4th of July weekend with Nick's family - including his brother Joe and his fiancee Sophie Turner, as the four of them enjoyed a bike ride on the Upper West Side of New York City.
The brunette beauty then joined Nick's whole family - including brother Kevin Jonas, sister-in-law Danielle Jonas, and nieces Alena and Valentina - in the evening on a private roof terrace to watch the fireworks.
The insider added: ''Nick loves doing things together with his brother Joe and Sophie, and the four of them love to hangout. Priyanka is a really good fit into the Jonas family.''
However, despite the good signs there aren't any plans for them to ''rush to the altar'' or go for a quick engagement, following Ariana Grande and Pete Davidson's high profile whirlwind romance.
The source explained: ''Everything has been going very smoothly between the two, but they aren't in a rush to the altar anytime soon.
''They are enjoying getting to know each other, but are definitely still inseparable since going public with their relationship.''