The 26-year-old rapper, who has been dating the 'Love Me Harder' hitmaker for six months, admits he hopes to marry her and start a family in the future, but insists they are in no rush.
Discussing their relationship, he said: ''It's pretty serious.''
Asked if the 21-year-old beauty is going to ''get married,'' the star - whose real name is Sean Michael Anderson - smiled and told 'Larry King Now': ''Aw, man. Not right now.''
But when the 81-year-old chat show host said: ''Get a Little Sean someday?'' the 'Dark Sky Paradise' hitmaker responded: ''Eventually, that's the goal.''
Big Sean previously admitted he appreciates ''every moment'' with Ariana and can talk to her about anything because they were good friends before they started dating.
He said: ''It was cool to have a girl that I could talk to about my problems. I did that with her. It's not some fake-a**, inauthentic s**t when I say we were friends. This is something special and I appreciate every moment of it.''
The rapper split from ex-fiancée Naya Rivera last April.
The 'Glee' star recently announced she is expecting her first child with husband Ryan Dorsey, who she married last July after a whirlwind romance.
All I Want For Christmas is widely regarded as one of the best festive tunes every year
Pearl Jam announced 14 dates in the UK and Europe in June and July 2018.