The England international started successive Premier League games for the first time since 2014 as Flanagan helped the Reds secure a 2-1 victory at Crystal Palace on Sunday afternoon.
You can see he is a Liverpool academy player. I am delighted he is back and playing
The 23-year-old defender has endured an injury-hit 18 months for the Merseyside outfit after Flanagan suffered a serious knee injury in the summer of 2014.
Flanagan made his first appearance in 619 days in Liverpool’s 3-0 win against Exeter City in the FA Cup in January.
Former Liverpool defender Carragher believes the Reds youth graduate should be offered a new long-term deal with the 18-time English champions.
“He shouldn’t get a contract because he’s a local lad,” Carragher told Sky Sports.
“He should get a contract because he is a good player. The local lad thing is a bonus.
“You can see he is a Liverpool academy player. I am delighted he is back and playing.
“The big disappointment for the supporters and Jurgen Klopp is that they have not included him in their Europa League squad so he won’t be able to face Manchester United.”
Roberto Firmino and Christian Benteke cancelled out Joe Ledley’s opener to secure a 2-1 victory after James Milner was sent off in the second half at Selhurst Park.
Liverpool are in seventh place in the Premier League ahead of their next top-flight game on 20 March.
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