Llorente scored twice in four minutes after the break to put Swansea two up before Roberto Firmino bagged a brace to draw Liverpool level.
But Gylfi Sigurdsson scored from close range with 16 minutes left to give Swansea a 3-2 win.
And after the match Clement insisted Llorente was crucial to Swansea’s Premier League survival.
Clement said: “Am I afraid to lose him?
“I want to keep him here.
“And the reason I want to keep him here is what he showed today.”
Chelsea boss Antonio Conte wants to bring Llorente to Stamford Bridge to provide cover for Diego Costa.
Costa missed the 3-0 win at Leicester last week after he became unsettled by a £30million-a-year offer from Chinese side Tianjin Quanjian.
But the striker has now returned to first-team training and is expected to feature against Hull tomorrow.