Indeed, on Twitter after United's 1-1 draw with Arsenal, the club icon and Sky Sports pundit responded to a fan who asked him about the Spaniard's future.
And Neville's reply was one of 'hope,' although the former Manchester United right-back feels the 'media noise' with regards to the goalkeeper is too big to ignore.
@GNev2 Do you think that's the last we will see of Dave in OT— Jack McGowan (@MackerNo11) May 17, 2015
Meanwhile, on the game more generally, Neville feels United were the more dominant team for 60 minutes at Old Trafford.
The pundit was impressed by Arsenal's comeback in the last half an hour, however, as the Gunners equalised late on to force the point against United.
The result should see Arsenal secure third in the Premier League, although it depends on their last two games.
Neville added that the transfer window should be interesting for Manchester United - a sentiment that would also apply to shot stopper De Gea.
United the better team for 60 min. Arsenal better for last half hour.Job done for United this season.Transfer window should be interesting— Gary Neville (@GNev2) May 17, 2015
Manchester United will finish their league season against Hull City knowing that Hull boss Steve Bruce has never beaten the club as a manager. Arsenal will face Sunderland and West Brom.