Arriving in January, Pogrebnyak joined Fulham from Stuttart on a short-term loan deal as cover for Bobby Zamora, who left for west London rivals QPR.
After scoring five goals in as many games, the 28-year-old striker has attracted interest from home and abroad.
Pogrebnyak’s contract with the Bundesliga side expires in the summer and Jol believes the Russian will choose to join Fulham over other sides
Jol told reporters: “I think he wants to stay because Pavel knows football.
“Things were not always easy for him [in Germany] but now he is the main striker for us. Hopefully he will appreciate that."
Key man Clint Dempsey has just one year to run on his contract and Jol is confident on the American putting pen to paper on an extension.
“We want to keep [Dempsey] but we have time on our side,” the Dutchman added.
"We have a year from June, which is why I tell you we have time on our side. It depends on him as well, maybe he wants to wait."
However, among talk of adding to the squad’s ranks, Dickson Etuhu is rumoured to be looking for a way out, but Jol moved quickly to quash any speculation.
The boss continued: "The strange thing with Dickson is that we get on very well. Two hours after the comments were made in the paper he came up to me and says he wants to stay.
"He wants to play here, he wants to fight for his spot and I like the boy.
"Maybe a couple of months ago when he was unhappy he told someone in Nigeria - I don't know where it came from - but he has issued a statement on the website.
"But even if hadn't put something on the website, it is no problem with me because I can get on with him very well."