The 28-year-old was drafted in on January transfer deadline day to fill the void left by Bobby Zamora's move to QPR but few could have predicted the on-loan striker's impact.
Pogrebnyak has netted five times in as many games for the Cottagers, leading to reported interest from rival Barclays Premier League clubs and some further afield.
The Russia international will be a free agent at the end of the season when his contract with parent club Stuttgart expires and Jol believes he could well stay in west London.
"Yes [I am confident of signing him permanently]," he said. "I told him [on Wednesday] and he wanted to come to my office at one o'clock [on Thursday] but I now realise that is impossible because I am here at the press conference.
"I want to speak to him first [before sorting out a contract]. I think he wants to stay because Pavel knows football. Things were not always easy for him but now he is the main striker for us. Hopefully he will appreciate that."