The Senegal attacker arrives back from the Africa Cup of Nations on Monday evening, as the plane that owners FSG had put on for his return was not able to depart on Sunday.
“The club did an outstanding job to bring him back as soon as possible and he is now on his way,” said Klopp on Monday.
“We thought it would be possible yesterday: we had a plane there but he was not allowed to go in the plane so we had to wait.
“He will be here tonight but I spoke to him and it is all good so far.
“He will be in tomorrow morning and we have to make a decision. We have to look in his eyes and see whatever is possible.”
Mane arrives back after being eliminated from the AFCON in the quarter-final on Saturday night against Cameroon, with the Liverpool attacker missing the deciding penalty kick in a shootout.
“I wish he hadn’t missed the penalty but he did and now he’s coming back,” said Klopp. “He’s a kind of an option for Chelsea. He’s back at least for the Hull game, that’s of course good for us.
“We have a very good player back for selection, that’s only good news.”
Liverpool have won just once, against League 2 Plymouth, in the seven games without Mane.
“He’s a quality player and it’s easier if you have him in the team,” said Klopp. “But you can’t expect him to decide games by himself.”
Judging by Klopp’s comments, and that Mane returns from Africa only 24 hours before the match, it seems very unlikely he’ll start on Tuesday night.