Manchester United are the favourites to land Sanchez after Manchester City reportedly pulled out of a deal for the Chilean.
City were not willing to offer more than £20million for Sanchez which has allowed United to storm ahead of their rivals in the race for him.
United are prepared to offer Henrikh Mkhitaryan to Arsenal as part of the deal for the 29-year-old.
But Neville cannot understand why City are not willing to offer more money for a player they have wanted to sign for the last year.
“The reports are suggesting he’s going to sign for United in the next few hours or 24 hours,” he said on Sky Sports.
“As a United fan I still can’t believe it. There was no inkling whatsoever that Alexis Sanchez was going to end up at Manchester United.
“I still think that Manchester City will wake up and offer the extra money and they will get him.
“That’s my mind, just speaking emotionally because he’s been City’s player, everyone knows he’s been City’s player for six, seven months.
“I don’t quite get this ‘City are walking away by not paying’.
“We’re talking about here City offering £290,000-a-week and United offering £350,000.
“City over a ten-year period, whether it be for (Dimitar) Berbatov, whether it would be for (Samir) Nasri, whether it’s for (Carlos) Tevez have fought Manchester United tooth and nail for many players and have always stood up to the task on money.
“Why all of a sudden are they saying no to a player, to be fair, is relatively cheap in the overall package terms?”