Grygera has had an unfortunate time of it at Craven Cottage, impressing with his early season form before succumbing to a serious knee injury in November which ruled him out for the remainder of the season. He suffered ruptured knee ligaments in a tie with Tottenham Hotspur and his resilient displays throughout August, September and October are now but a distant memory.
And, with the Czech's deal set to run out in June, Jol is wary of jumping in to a new contract too quickly and is keen to assess Grygera before anything concrete is put on the table. The opportunity, though, says Jol, is still there to prove his worth to Fulham.
Speaking to the Fulham Chronicle, the Dutch manager said: "I feel we owe it to him to keep him here and get him fit, and then we can make a decision, or he can if he has other offers.
"The main thing for him is to get fit. That won't be until the middle of July and then we can make a decision.
"He did well from the first match, which is very unusual [for a player new to English football]. I was very happy with him.
"He can play left-back, right-back or centre-back, but it's not a minor injury. It isn't easy to come back to full fitness if you're that age."