Since retiring from football in 2011 the former Manchester United and 85-cap England defender has combined work as a Sky Sports pundit alongside work as Hodgson's assistant manager -- roles for which he has been lauded.
Neville, however, acknowledged that he could not commit to both jobs long-term and had a "decision to make in the next 18 months."
Neville may be tempted to pursue punditry following the Premier League's staggering 5.2 billion pounds ($7.93 billion) TV deal, of which Sky paid 4.2 billion for 126 live games a season from 2016 to 2019.
Former Liverpool defender Jamie Carragher has also opted for a career in punditry after hanging up his boots in 2013.
"That's the coaching badges out the window for a few years," Carragher said on Twitter upon hearing news of the new Sky Sports deal for Premier League coverage.
Arsenal's all-time record goalscorer Thierry Henry has recently joined Sky's stable after bringing an end to his playing days, while others like former Liverpool players Jamie Redknapp and Michael Owen are also regulars in the TV studios.
Neville already holds Uefa A and B licences and is currently completing his coaching Pro-Licence and could be a future England manager Hodgson said.
"If you're asking me would I like to see Gary Neville in coaching or management then, yes, I would.
"It is up to the FA to decide what his value to England is in the future. He is a very good coach now and he will become an even better coach with experience.
"From a selfish point of view I personally would see him being more valuable to me as a football lover than as a pundit.
"Punditry is not that difficult if you know a bit about football. You don't win and lose in punditry."
Hodgson, 67, has two years remaining on his current deal but refused to be drawn on what his future holds after the 2016 European Championships in France.
"We'll see. At the moment I feel good and I hope that will continue for a few more years," he said.
"When the day comes I will know what the right time is and I'll do it but I have an important job to do."
($1 = 0.6558 British Pounds)
(Reporting By Tom Hayward; Editing by Michael Hann)
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