Henderson joined Liverpool from Sunderland in the summer of 2011 for a transfer fee reported by The Daily Mail to be worth £20 million.
Rodgers, who was appointed as the Celtic manager in the summer of 2016, was in charge of Liverpool from 2012 until October 2015.
The former Swansea City manager told The Telegraph: “There was a lot of interest in Jordan so I invited him around and chatted.
“I said to him, ‘Jordan, you are going to be the next captain of Liverpool’. That was it from there. We spoke about moving forward.
“It was a natural move for him as Steven Gerrard was preparing to leave. I knew he would be a captain the club would be proud of.”
Development and progress
Henderson - who earns £105,000 per week as salary, according to Spotrac.com - did not start his Liverpool career strongly, but in recent years the former Sunderland star has established himself as a key player for Liverpool.
The 28-year-old, who helped the Reds reach the final of the Champions League last season, has been a key figure for England at the World Cup in Russia, as the Three Lions have progressed to the semi-finals of the competition.
Another Liverpool player who is doing well in Russia is Dejan Lovren, who has helped Croatia to the semi-finals of the World Cup.
The 29-year-old centre-back will come up against Tottenham Hotspur and England international striker Harry Kane in the semi-final on Wednesday, and he is looking forward to the challenge.
“He is one of the best strikers in the world, but I like to challenge these strikers and to show to everyone that I am one of the best defenders.”