The Athletic Bilbao striker, who recently agreed to join Juventus on a free in the summer, will have the scan to assess a sprain picked up during training on Saturday.
Llorente had been due to play for Athletic on Sunday against Atletico Madrid, in a match that would mark his first appearance at San Mames since the announcement he would join Juventus on a free in the summer.
However, the club released a statement on its official website to say that Llorente would be unavailable due to the injury.
“Llorente suffered a sprain to his right knee during the latter part of Saturday's session.
“On Monday, January 28 he will have an MRI scan to evaluate the damage.”
There has been constant speculation about the Spain international's future throughout the current season, with Llorente only starting one league game for the Basque outfit as a result of his public decision to leave at the end of his contract.
Juventus reportedly had to fend off interest from several Premier League clubs to agree a deal with the striker, who will complete his move to Turin in the summer.
After reaching two cup finals and finishing 10th in the league last season, Athletic has struggled in La Liga this time around, and sits 15th in the division ahead of the match against high-flying Atletico on Sunday.