The Reds face a goalkeeping injury crisis after one of their own fans injured Adrian during the shootout celebrations.
He was left with a swollen ankle after a supporter who invaded the pitch to join in their celebrations slipped and kicked his foot, Liverpool manager Jurgen Klopp explained.
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"When we were all together (celebrating after the match), a supporter jumped over something, was chased by some security guys, slipped and kicked his (Adrian's) ankle," Klopp told a news conference.
"So yesterday it was swollen -- today it is better, but we have to see... it would help him a lot if it was 100% clear he can play tomorrow... it's not funny.
"He will not go for a scan. We wait for the swelling to go down. It went down already. You can imagine, you have that and then you fly four hours back and that doesn't help swelling."
But the Spaniard, signed on a free transfer from West Ham to provide cover for Alisson, has given an update on his condition.
"Today I feel much better.
There were fears that Adrian would not be able to play against Southampton
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"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 made me a tackle 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."
When asked if he will be fit for the trip to St Mary's, Adrian added: "Yeah, I think I have many chances.
I feel mentally ready and I also hope today with the treatment of the ankle it's going to be much better. But I'm very optimistic to start playing tomorrow again.
The setback had left Liverpool with the prospect of being short of their two main keepers after Alisson was injured during the opening game of the season, but Klopp said back-ups Lonergan and Caoimhin Kelleher were ready if needed.
"We need to think about Saturday to find a way to win the game. Andy Lonergan is in training with Kelleher and we have them if we have to make a decision," Klopp said.
Liverpool celebrate winning the European Super Cup
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"Adrian was a week before, Lonergan has trained with us. Kelleher has potential but is not 100% yet. We'll see."
Lonergan has never played Premier League football, but has over 400 appearances in the lower divisions. He spent part of last season on loan to Rochdale in League One, and made four appearances for former parent club Middlesbrough.
The 35 year old signed for Liverpool after first choice goalkeeper suffered a calf injury in Liverpool's first Premier League game this season against Norwich City, and went on the pre-season tour with the club to provide cover.