The No.20 missed the weekend’s dramatic 2-1 win at West Bromwich Albion due to a foot injury sustained at Manchester United three days earlier.
Initial assessment suggested Jota would miss the remainder of the campaign; however, further diagnosis has shown the issue is not as severe as first feared.
Klopp told his pre-Burnley press conference: “Diogo, when the swelling went down, we did another picture and it looked better than in the first place with the first scan. With the CT [scan] you could see it better.
“So, there is a tiny, tiny little chance for him for the weekend, but it depends how it improves now. We have to see that.
“It is obviously good news for Portugal and for Diogo himself, with the Euros not in danger at all. That’s good, but if it’s good enough for us, we will see.”
Elsewhere, Alex Oxlade-Chamberlain should return to Liverpool’s squad for the trip to Turf Moor on Wednesday night, while James Milner will be assessed.
Naby Keita will miss the clash with Burnley, however.
Asked if any players were set to return, Klopp said: “Millie will train today but is that then enough for being involved tomorrow? I will see.
“Ox was ill, [so] yes, Ox is back. Naby wasn’t part of team training yet so that will not be enough until tomorrow for sure. Ox was in team training so he is back.”