Fulham have won four of their last six league games and moved level with eighth-place Liverpool on Tuesday after registering their first ever win at Anfield.
The Londoners currently have 49 points - four short of their club record, which was achieved in 2009 while England manager Roy Hodgson was in charge.
Jol's team host Sunderland on Sunday and then travel to Tottenham on the final day of the season and the Fulham boss thinks beating the club record is a serious possibility - something he would regard as an amazing achievement considering that they have played 14 Europa League games this term.
"If we can get six points it will be 55," Jol said.
"First we said 40, then 50 and it almost looked undoable, but now I think we are in a fantastic position to get even more points on the board.
"In 2009 they got 53 but I think in that season they didn't play in Europe, and the season after they did and it cost them some points.
"This year we played in Europe so to have 50 points or more after playing in Europe would be fantastic."
Fulham's current position would have been unthinkable at the start of the campaign, when Jol's position came under scrutiny after it took until October for the Dutchman to register his first league win since his appointment.
The 56-year-old has masterminded a big turnaround in fortunes since and has got the best out of players like Clint Dempsey and Damien Duff while making the hugely effective loan signing of Stuttgart forward Pavel Pogrebnyak.
Had the club not had the rigours of playing in the Europa League to deal with, Jol reckons his team could be fighting the likes of Chelsea for a top-six finish by now.
"We did well after Christmas, maybe after being out of the Europa League," he said.
"I think if you look at the stats we would be in the top six or something. Our good form is not just over the last six games."
The west London club lead Sunderland by three points ahead of Sunday's game.
The Black Cats have won just once in their last 10 games in all competitions, but their position of 11th in the table is a vast improvement on their predicament in December when Steve Bruce was sacked with the club hovering just above the relegation zone.
"They have done ever so well. Martin O'Neill has got some great results, although maybe not so good over the last month or so," Jol added.
"To stay in the top 10 is what we want but of course they want the same thing."
Striker Andrew Johnson missed Fulham's games at Liverpool and Everton due to an adductor injury and will be absent again on Sunday.
Jol himself missed the two games on Merseyside due to a chest infection but will be back in the dugout after making a full recovery.