The Three Lions lost to Italy on penalties in last year's European Championships quarter-final, the latest exit from a major tournament in such a manner.
The FA have appointed Reddin - who helped Jonny Wilkinson during England's 2003 rugby union World Cup triumph and who also worked with Team GB at the 2012 London Olympics - as their new head of performance services.
Reddin will take up his role early in the New Year and Hodgson admits he is keen to speak to him, having an 'open mind' regarding how to improve penalty taking.
The England boss told the Sunday Express: "I'll be interested to see what Dave has to say on the subject.
"He was heavily involved with that part of sporting life with the Olympic team, and he's worked in rugby where kicking penalties is a crucial part of the sport. You only have to remember Jonny Wilkinson winning the rugby union World Cup final with his kicking.
"So, I have an open mind on the subject, I really have. When we lost on penalties at Euro 2012 I thought fatigue was the major factor. That was my personal experience.
"We had to work so hard over 120 minutes to keep Italy at bay in that game. We did an awful lot of running.
"But I can't say that the mental side played no part. That would be nonsense. Then mental side plays a major part in football, full stop.
"Whether someone who's a trained psychologist can help a player shoot better from a penalty, or whether coaches and managers can help - that's a discussion. Maybe there's a blend of the two."