The Premier League club confirmed the sad news on Saturday, with Joe Bradley passing away three days after his son's first senior goal for the Reds.
Bradley was named man-of-the-match for his performance in Wednesday's 4-1 victory over Chelsea, with the full-back also providing two assists at Anfield.
His father then passed away at home in County Tyrone on Saturday morning, with reports in Northern Ireland saying it came following a battle with illness.
Liverpool confirmed the tragic news with a brief statement: "Liverpool FC is deeply saddened by the death of Conor Bradley's father, Joe, today.
"The thoughts of everybody at the club are with Conor and all of the Bradley family at this very difficult and sad time.
Read more on Liverpool
Bradley scores first Liverpool goal, equals Fernandes and Jesus assist totals
Prem star, trusted Alonso youngster and no Salah - How Liverpool could look after Klopp
"On behalf of Conor, LFC strongly urges that the family's privacy is fully respected at this time."
Liverpool play Arsenal at the Emirates Stadium on Sunday, with the Reds squad making the trip to London on Saturday ahead of the match.
There has been no comment over whether or not the defender will be involved in the Premier League fixture.
Manager Jurgen Klopp praised the youngster's ability and attitude following his display against Chelsea, with Bradley emerging as the next bright young talent to emerge from Liverpool's academy.
Most read in Football
Kane equals another Bayern Munich goal record as star continues stunning form in Germany
'Flappy' Vicario questioned as Spurs 'show why they can't be considered title contenders'
Two Chelsea players quit social media after abuse following Liverpool hammering
Tottenham 'one of two Premier League clubs eyeing Raphinha' amid Barcelona doubts
The Northern Irishman was also named man-of-the-match for Liverpool's FA Cup fourth round victory over Norwich last Sunday, where he assisted another two goals.
"What a wonderful kid he is," said Klopp, who was pictured embracing the 20-year-old after the full-time whistle.
"Outstanding finish, the whole game, the contribution, the involvement. It's a job to play against [Raheem] Sterling, that's not easy. I'm really happy for him.
"He's a very serious young man and that was pretty special I have to say. We saw in pre-season. He is really doing well."