The Whites host the Clarets - who sit five points behind their hosts in the first top flight relegation spot - at Elland Road following a 15-day break from on-pitch action.
United have been ravaged by injuries in recent months, seeing no fewer than 10 senior players missing against Arsenal last time out due to knocks, suspension and Covid.
Games against Liverpool and Aston Villa were postponed over the festive period, falling by the wayside due to a small coronavirus outbreak in West Yorkshire.
Llorente missed the hosting of the Gunners last time out after testing positive for the virus ahead of kick-off.
The Spain international will, though, return to Marcelo Bielsa's squad against Sean Dyche's men and wants Leeds to break a three-game losing streak to begin 2022.
"It will be a huge step for us because we have to start the new year with a good result," Llorente told Radio Leeds.
"At Elland Road, we have to win the match because the supporters are amazing. We have to use this help that the supporters give us. The most important thing for us is to start the new year with a victory.
"We were in a hard situation because we had problems with Covid, with injured players. I think that now we are in condition to play Sunday’s game so the most important thing is to be focused on Sunday’s game against Burnley. "
Llorente, if selected, should face former Whites striker Chris Wood.
Asked about facing the forward on Sunday, he said: "He [Wood] is an important player for them, so we try to avoid letting them control the ball in the area, avoid crosses, these types of things. His style, to avoid all of this."