The Ridin' Solo singer, 30, and the influencer are said to be isolating together in his Los Angeles mansion, California, during the covid-19 lockdown.
Jason and Jena haven't publicly commented on the dating rumours but they have been sharing energetic workouts videos together on their Instagrams.
Since March, the duo have been posting TikTok clips of themselves performing impressive fitness moves.
A source told The Sun: 'Jason and Jena hadn't been together too long before the lockdown started but they decided to take the plunge — and they are loving it.
'They're both outgoing, lively and spontaneous, so they're a really good match.
'For a while, Jason didn't want to be stuck down in a relationship, especially when performing around the world. But this just felt right and he is seeing what happens.'
They added that it is 'going well so far' and the duo have a 'really good connection'.
Jason's most recent romance was with lingerie model Daphne Joy in 2016.
Prior to this, he dated singer Jordin Sparks for three years until they split in 2014.
While Jena, whose Instagram boasts 3.8 million followers, previously dated Manchester United player Jesse Lingard with the two splitting in March 2018.
Jason is typically private about his love life and in 2017 he said: 'I've seen that now, that it's never worked in the spotlight. I've been [single] forever. So now I'm going to try something different.
'If something does happen, I'm not going to do it with everybody watching. I'm going to be as private as I can be. Of course, it's hard because you're in the public eye but we can be a little more private.'
