The 21-year-old tore the anterior cruciate ligament in his right knee early in Madrid's Champions League match with Schalke on March 18 and subsequently underwent an operation at the Augsburg clinic of knee specialist Dr Ulrich Boenisch.
However, in a statement on Friday Madrid revealed Jese had been suffering from a fever and inflammation of the affected knee.
"Real Madrid player Jese Rodriguez will shortly travel to the Hessingpark-Clinic in Augsburg to undergo a medical revision with Dr Ulrich Boenisch after inflammation was detected in the operated knee, as well as a fever," a club statement confirmed.
Jese sustained the injury after just two minutes of last month's 3-1 win over Schalke in the second leg of their last-16 tie, following an innocuous-looking tussle with Sead Kolasinac.
He was carried off on a stretcher to be replaced by Gareth Bale before being taken away to hospital, where tests revealed the extent of the damage, which is expected to sideline him for at least six months.
Jese had been enjoying a fine season at Madrid, and had scored five goals in his previous six starts for the club prior to being named in Carlo Ancelotti's first XI for the second leg with Schalke.
Such had been Jese's impact this season that he had been talked about as a possible contender to go to the World Cup with Spain, even though he has yet to make a senior appearance for his country.