Vettel and Alonso are expected to both challenge for the F1 title next season.
Vettel came second in the 2017 Drivers’ Championship, behind winner Lewis Hamilton, while Alonso was way off the pace.
Alonso is expected to improve next year when McLaren swap their Honda engine for Renault.
But Vettel was in no mood to speculate over the Spaniard’s potential success in the new car.
Asked by Spanish newspaper AS if Alonso can challenge for the title, the German replied: “I do not care.”
It was a curt response from the four-time world champion, whose Ferrari is also expected to improve next year.
Vettel was at one stage leading Hamilton by 14 points in the Drivers’ Championship battle.
But the Mercedes driver hit back after the summer break to claim the trophy.
Quizzed on what was the most annoying question he has been asked recently, Vettel said: “Why did not I get the title? Why did not I become a world champion again?
“That implies that you could have done something about it.
“If the same question arises again and again, it can be annoying.”