The former United defender used the situations of Luis Suarez, Steven Gerrard, Jordan Henderson and Raheem Sterling to underline the need for the Reds to sort the futures of their best players earlier than they have done in recent months.
“From Liverpool's point of view, I don't think they have particularly handled contracts well over the last 18 months," Neville told Sky Sports.
"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.”
Neville made the comments in the aftermath of news that Sterling wants to leave Liverpool in the summer transfer window.
Sky Sports claim that Liverpool will not sell Sterling in the summer, but it remains to be seen if they can force the 20-year-old to remain at Anfield.
Neville does have a point about the Merseyside outfit sorting out the futures of their key players early.
However, one needs to remember that contract negotiations take time. Sterling’s current deal runs out in June 2017, and from Liverpool’s point of view, there is nothing else they can do other than offer a deal to him.
Liverpool have done that, but it is Sterling who is not willing to sign, as he told BBC Sport back in April that he had turned down a contract worth £100,000 a week.