The Portuguese international has missed Liverpool's last eight games in all competitions due to a hamstring injury but has returned to training ahead of schedule. However, Klopp has confirmed that he doesn't know yet if Jota will be in the matchday squad for the Reds' trip to Turf Moor.
He said (quotes via Liverpool's official website): "I don’t want to rule out anybody now. We will see. He didn’t train with the team yet and we have only one proper session, so it would be a surprise – but maybe I will be surprised and all fine. I don’t know.
"I saw him [on Friday]; he didn’t train with the team but the session I saw was really intense, but I didn’t ask yet who will be available. The medical department will tell me and then I will know more."
The likes of Cody Gakpo, Luis Diaz and Darwin Nunez haven't been prolific in front of goal this season, with the trio registering just nine Premier League goals between them so far. Mohamed Salah has almost single-handedly carried the Reds' frontline in recent weeks, with the Egyptian winger also on target in the 1-1 draw against Arsenal.
Jota's return could prove to be a timely boost for Klopp as Liverpool aim to return to winning ways after successive home draws against Manchester United and Arsenal. The 27-year-old scored eight goals in all competitions before his injury - four in the Premier League - and will undoubtedly give Liverpool the cutting edge they have lacked in recent weeks.
While Jota has an outside chance of featuring against Burnley, the Reds will be without Joel Matip, Andy Robertson, Thiago Alcantara, Alexis Mac Allister, Kostas Tsimikas and Stefan Bajcetic for the trip to Turf Moor.