When Keane was asked if he had anything to add, the Sky Sports pundit said he was "Just listening", before adding: "There's a good vibe going on."
Ten Hag then joked: "Oh, you don't want to spoil the vibes, no?", as a slightly cringy exchange began.
The Irishman, who heavily criticised the club last season amid their worst-ever Premier League campaign, said: "Not tonight, next week, next week," to which Ten Hag said: "I know, thank you."
Keane finished by warning: "I'll be waiting...Just keep winning, it's easy, it'll be no problem," before the Dutchman quipped: "It's so simple."