The Spaniard, who was a hero in the 5-4 penalty shootout victory over Chelsea after saving Tammy Abraham's penalty to clinch the win, has a swollen ankle caused by the fan sliding into him. The fan was trying to evade security at Vodafone Park in Istanbul.
Jurgen Klopp, who is already without first-choice goalkeeper Alisson due to a calf issue, revealed it is not "100 percent clear" whether Adrian can feature at St. Mary's.
"When we were all together, a supporter jumped over, was chased by some security guys, slipped and kicked [Adrian's] ankle," Klopp told a news conference. "Crazy! Yesterday it was swollen and today I spoke to him and he said it's much better, but we have to see.
"He couldn't have played directly after we landed in Liverpool, but I saw him now, he's better."
Speaking to Liverpoolfc.com on Friday, Adrian gave an update on his condition.
"Today I feel much better," he said.
"It was a strange, weird situation because we were celebrating between us and one guy jumped from the crowd and started running.
"I think he slipped in front of us and also the security with him and tackled me from the side. It was a bit of a strange situation but I feel much better today and I hope [I'm] ready for tomorrow."
Adrian was unexpectedly drafted into action during the first half of the 4-1 win over Norwich on the opening day of the Premier League season after Alisson limped off.
Yes mate, getting better every day! 💪🏼— Alisson Becker (@Alissonbecker) August 16, 2019
Adrian -- recruited as a free agent on Aug. 5 -- wasn't afforded time to settle before featuring, but Klopp saluted the former West Ham keeper's "big personality."
Andy Lonergan, who trained with Liverpool during their preseason tour of the United States, was signed on a short-term deal as experienced cover earlier this week with highly rated young keeper Caoimhin Kelleher shaking off a wrist injury.
Asked if Lonergan or the 20-year-old Kelleher could start against Southampton, Klopp said: "If we have to make a decision, then we make a decision.
"Caoimhin is a boy we are all excited about. He's now in training, but not 100 percent yet. He has to be in training today, then we will see."
Meanwhile, Naby Keita will sit out the game due to a hip muscle injury that Klopp labelled minor, but he could not put a time frame on the midfielder's return.