Berbatov, 31, moved to Craven Cottage in the summer after a four-year spell at United which saw the Bulgarian experience the highs and lows of a modern footballer.
After finishing as the Red Devils' top goalscorer the last time they took the Barclays Premier League title in 2011, Berbatov found himself well down the pecking order behind the likes of Robin van Persie, Javier Hernandez and Danny Welbeck.
Jol, who worked with Berbatov at Tottenham, moved to take him to Fulham before the end of the summer transfer window but will not challenge the player to show United what they have lost by letting the former Bayer Leverkusen man leave.
"I don't want to put pressure on him," Jol said. "Of course if he was playing for Man United it would be a bit easier for him but he is not playing for them any more, he plays for us.
"Hopefully he will do something nice, but for me it is important that he works for the team. We would love to go to the next round, even though we are playing against United."
Berbatov is likely to be the focal point of Fulham's attack on his first return to Old Trafford, but Jol is not telling his star name to try to prove a point.
"That would be unfair because he can't do it on his own," he said.
"If we get a good day there maybe we could end up with a surprise and you never know, hopefully he will come up with something out of the blue, but that is the same for all of my players."