The England international is reportedly set to tell the five-time European champions that he wants to leave Anfield in the summer transfer window.
I don’t think it’s a case where all is lost
Sterling was speculated to have rejected a £100,000-a-week offer from Liverpool earlier in the season amid reported interest from Arsenal, Chelsea and Real Madrid.
Former Manchester United defender pointed out Steven Gerrard’s famous u-turn after he came close to leaving the Reds before he eventually rejected Chelsea’s advances in 2005.
“I’ve seen these situations turn around, where a player can be happy again,” Neville told Sky Sports.
“I don’t think it’s a case where all is lost. It’s about communication, getting themselves in a room and sorting it out.
“Steven Gerrard had his ups and downs along the way, there were moments where, could he have left, might he have left, he thought about leaving… it wasn’t all plain sailing.
“If you look back through careers of football players, even players who have been one-club men and stayed at the club, there are ups and downs and obstacles along the way. This could just be an obstacle.”
The 20-year-old has two years remaining on his current deal that he signed in December 2013.
Neville added that Liverpool must improve how they negoatiate contracts with their players.
“From Liverpool’s point of view, I don’t think they have particularly handled contracts well over the last 18 months,” Neville added.
“You think of Steven Gerrard. I know we’ve given him a great send-off this weekend and it’s rightly deserved, but that could have been handled a little bit better, someone who, had he been handed a contract a year ago, probably would have signed.
“With Luis Suarez, it seemed a bit strange in the way his contract was dealt with and he ended up leaving. Jordan Henderson has signed now but that seemed to drag on a little bit as well. Now Raheem Sterling.
“Liverpool need to nip it in the bud. It’s three or four times this has happened in the last couple of years, so they may have a little issue they need to deal with themselves on how they go about doing this internally.”
Sterling has scored seven goals and has made seven assists in 35 Premier League appearances this season.
The England forward emerged as a regular first-teamer under Northern Irishman Brendan Rodgers.
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