Jol revealed the potential extent of the injury Diarra suffered making his return from international exile with Mali this month.
The 31-year-old, who had not played for his country for more than a year, damaged his left knee and was forced to miss Fulham's 2-0 Barclays Premier League win over West Brom last weekend.
Jol confirmed on Thursday that Diarra requires some form of surgery and will miss at least another three weeks.
But if it transpires he has damaged his cruciate ligament, he could be out for five months.
Jol, who was expecting to learn the true extent of the damage next week, said: "There's a little piece of cartilage floating in his knee, so we have to operate that in any case, and that can be three or four weeks.
"But if there is damage to his cruciate ligament, for example, it will take a lot longer.
"It will take him three, four, five months at least."