The Brazil international is understood to be close to sealing a switch to Camp Nou in excess of £130m, having failed to push through a move during the summer window.
Former Reds defender Jamie Carragher commented earlier this week that the Merseyside outfit should do all they can to delay a transfer until the 2017-18 season comes to an end, and Neville - speaking to Sky Sports News - is in full agreement.
"I have been tweaking the tail of the tiger with my tweets to Jamie Carragher about the Philippe Coutinho situation and actually agree with his suggestions that Liverpool should do a deal with Barcelona for the summer," he said.
"To have turned down a bid in the summer and then lose him now would be madness. You're always likely to lose a player when Barcelona or Real Madrid come calling. There's an inevitability of him leaving but they need to say 'give us time'.
"To lose him now could have a terrible impact on their season. Liverpool are too big a football club to let one player mess them around. To be fair, I wouldn't say they won't make the top four if he goes, but the impact off the pitch and in the dressing room - along with a loss of skill on the pitch - will be huge.
"There's also their troubles with breaking down deep-lying defences, which was clear when you looked at the Everton game when they left him on the bench. It also just sends completely the wrong message and I agree with Jamie: there will be a two-tier impact if they let him go now."
Coutinho has scored 12 goals and set up a further eight in 20 appearances for Liverpool this season.