The 'Dancing With the Stars' performer, who enjoyed a ''very flirty'' night out with the 'Booty' hitmaker in Connecticut last Saturday (21.06.14) after denying rumours they are dating on Twitter earlier this month, reportedly wants them to be more than friends, but is trying to respect her space so she can get over her recent split from Casper Smart.
A source told PEOPLE magazine: ''[They] are just friends, but I'm sure he'd love it if they were more.
''He really likes her. He thinks she's beautiful, really cool and down-to-earth.''
The duo were first introduced by Jennifer's close friend Leah Remini, who bonded with the professional dancer, 34, while appearing on the US dancing series last year.
The 'First Love' singer danced with Maksim - who previously dated Kate Upton - at the American Music Awards in November and they were ''inseparable'' at his brother Val's birthday party in Los Angeles in March.
The 44-year-old singer, who has six-year-old twins, Max and Emme, with ex-husband Marc Anthony, recently revealed wasn't looking for a new romance.
She said: ''I'm good right now. Let's just say we just got out of a relationship. There needs to be time for reflection and alone time.''
But the 'On The Floor' star previously admitted that she's ''one of those people who doesn't like to be alone.''
'Smalls Change (Meditations Upon Ageing)' arrives in April.
The two awards have made for a great 72nd birthday present for the country music icon.