It is widely expected both Saracens playmakers will be included in England's Six Nations squad, named on January 11, as new boss Stuart Lancaster looks to make up to 17 changes from the World Cup.
The 20-year-old's father is the legendary dual international Andy Farrell, who is the Saracens head coach and a newly-appointed member of Lancaster's interim England management set-up.
Hodgson, who has 36 Test caps, was expecting to mentor Farrell Jnr when he moved from Sale in the summer, but he has discovered a young man wise beyond his years.
"When I came here, (Saracens director of rugby) Mark McCall talked to me about passing on advice to him but the more time I have spent with him the more I have realised that he probably doesn't need to listen to me that much," Hodgson said.
"He is very mature and you can definitely see his dad in him. You can see the competitive streak in him straight away and he understands the game very well.
"He is not afraid to stand up and say what he thinks. He likes to take control of things, he is very good at feeding information to me during game time.
"He has definitely got the potential to play for England. He doesn't seem to be fazed by anything and seems to be in control of everything he is doing."
Farrell played at fly-half in Saracens' Aviva Premiership title-winning campaign last season and it will be his long-term positions.
But Saracens have shifted him into the centre this season with great success, partly to accommodate Hodgson's arrival at the club and partly to aid his own development.
Jonny Wilkinson learned his trade at inside centre before settling at fly-half and Farrell is doing the same now, although the Saracens structure means he actually wears the 13 jersey.
"He has built on massively from what he achieved last year, coming in halfway through the season and winning the championship," Hodgson said.
"Playing at centre gives him that bit more time on the ball, he has got the bigger picture of seeing what goes on and he has not always got that chaos in front of him playing at 10.
"Playing in any other position you get to appreciate your own position as well. He's playing very well at the minute, he's kicking his goals and doing everything that is required of him.
"You have to have a good balance in the midfield to not only be attacking threats individually but to be passing threats as well."
Having missed two World Cups through injury, Hodgson could not force his way into England's 30-man squad for this year's tournament in New Zealand.
With Jonny Wilkinson now retired, Hodgson is set to be named as Tony Flood's back-up for England's forthcoming Six Nations title defence.
"I am not the kind of person who would retire myself from international rugby. If someone wants to pick me then brilliant," Hodgson said.
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