Ings has been in isolation since that match and is due to come out of it on Friday ahead of their game with Leicester City.
Ings, 28, played 77 minutes and scored Southampton’s winner in the match at St Mary’s on January 4. He had tested negative before the game.
Ings celebrates with his Southampton team-mates after scoring the winner against Liverpool
The striker celebrated with his team-mate after netting the winner but Hasenhuttl confirmed there had been no other positive tests in his squad since.
Speaking ahead of Southampton’s trip to Leicester on Saturday evening, Hasenhuttl said: ‘Danny Ings is out now. He is in self-isolation. He may have been contagious against Liverpool. We have had no other positives since.’
Goalkeeper Alex McCarthy missed the Liverpool game after a positive test.
Liverpool have not announced any positive Covid results since their game at Southampton.
Ings’ positive test comes as football is under enormous scrutiny for how it is responding to the coronavirus pandemic and Whitehall sources have told Sportsmail there is ‘growing frustration’ over Covid rule breaches among players.
As an elite sport it is allowed to continue when most of the activities in the country are curtailed during the national lockdown aimed at reducing sky-high rates of coronavirus infection.
Ings, who may have been contagious during the game, is challenged by Thiago Alcantara
Ministers have considered shutting the game down and insist it is hard to justify the additional freedoms it enjoys when the public see footballers flouting the rules they have to follow, including group hugs, dressing room celebrations, as well as going to parties.
Seven Premier League players from five clubs breached social distancing guidelines by attending or organising parties during the festive period.
This was followed by breaches of Covid rules on and off the field in the FA Cup third round when players celebrated goals in huddles and enjoyed a singsong and drank champagne together in the dressing room after two matches.
And now, with the return of Premier League fixtures, players have marked the majority of goals with celebratory scrums, which have horrified health experts for the poor example they set and infuriated frustrated politicians. All of this has increased calls for the game to be shut down.
PREMIER LEAGUE COVID-19 TEST RESULTS FOR 2020-21 SEASON
Round 1: Aug 31-Sep 6 – 1,605 tested, with three testing positive.
Round 2: Sep 7-13 – 2,131 tested, with four testing positive.
Round 3: Sep 14-20- 1,574 tested, with three testing positive.
Round 4: Sep 21-27 – 1,595 tested, with 10 testing positive.
Round 5: Sep 28-Oct 4 – 1,587 tested, with nine testing positive.
Round 6: Oct 5-11 – 1,128 tested, with five testing positive.
Round 7: Oct 12-18 – 1,575 tested, with eight testing positive.
Round 8: Oct 19-25 – 1,609 tested, with two testing positive.
Round 9: Oct 26-Nov 1 – 1,446 tested, with four testing positive.
Round 10: Nov 2-8 – 1,646 tested, with four testing positive.
Round 11: Nov 9-15 – 1,207 tested, with 16 testing positive.
Round 12: Nov 16-22 – 1,530 tested, with eight testing positive.
Round 13: Nov 23-29 – 1,381 tested, with 10 testing positive.
Round 14: Nov 30-Dec 6 – 1,483 tested, with 14 testing positive.
Round 15: Dec 7-13 – 1,549 tested, with six testing positive.
Round 16: Dec 14-20 – 1,569 tested, with seven testing positive
Round 17: Dec 21-27 – 1,479 tested, with 18 testing positive
Round 18: Dec 28-Jan 3 – 2,295 tested, with 40 testing positive
Round 19: Jan 4-Jan 10 – 2,593 tested, with 36 testing positive