Manchester United winger Nani has arrived in Istanbul to complete a move to Fenerbahce.
Liverpool are set to confirm the appointment of Sean O'Driscoll as assistant manager on Monday.
The 21-year-old is in the penultimate season of his existing deal but, having established himself as a first-choice player after initially getting his opportunity due to Jose Enrique's injury, will be around for the long term if Rodgers has his way.
"Jon will be given a new contract," the Northern Irishman told national newspapers. "Come the summer he's got another year so he will definitely be given a new deal, no question.
"He has been outstanding. He reminded me of Steve Nicol against Manchester United on Sunday - a right-footed player on the left side, steady, aggressive, no fear.
"He's been a revelation, and particularly in the big games. It's great when you see a young player develop like that. You can see the confidence he has now. He has made himself an important member of the squad.
"He is young but his performance levels are so mature. They had to change (Juan) Mata over at the weekend, he booted Mata over to the other side and then (Adnan) Januzaj as well. He's not easily fazed. I think the biggest thing for me has been his temperament."
Flanagan has made 14 appearances this season, all as part of Rodgers' starting line-up, and scored his first senior goal against Tottenham in December.
Rodgers said: "He never really featured for me at all at the start, there was Jose Enrique and others considered in front of him. We spoke a number of times about him going out on loan but no one came in for him.
"I had (England Under-21 manager) Gareth Southgate down here and he was raving over him. He is a wonderful young talent but in order to stay at that level he needs to focus and concentrate on staying in the team.
"He thought the opportunity might have passed him by but now he is grabbing it with both hands and doesn't want to let it go. You can see the hunger and his quality in his performances."