The 27-year-old striker has refused to sign an extension to his Athletic Bilbao contract, and although he has since suggested he would be willing to talk to club officials in January, he has found himself sidelined by manager Marcelo Bielsa.
Llorente made the most of the substitute's berth he was given at the weekend as he came on to score the equaliser in a 3-3 draw at Espanyol.
That earned Athletic only their fourth point of the season, and Gorka Iraizoz is hoping they can find the rhythm they have been lacking by switching to the Europa League.
"We are playing at home, we believe in ourselves," he said. "We can get back on track with a win."
Athletic made it all the way to the final last season, and an opening fixture against Europa League group stage debutants Hapoel looks straightforward.
However, Iraizoz is cautioning against arrogance.
"The groups are always difficult," he added. "It's not just a cliche to say so. All the teams have their strengths.
"Last year we had the chance to play in the final, but although the road is long and you have to put in a lot of work, you have to believe you can reach the final."
Athletic have won both their home European matches this season during the qualifiers, extending their unbeaten home run in contintental competition to 11 matches.
Isreali champions Kiryat Shmona played in the qualifying rounds of the old UEFA Cup in 2008/09, their European debut, but this is their first time in the group stages.