However, even if they were to finish above their city rivals in the Barclays Premier League, the defender will not class that as success.
The Toffees have clawed themselves back up to eighth in the table, five points behind Liverpool, after a five-match unbeaten league run which has been achieved despite injuries to key players like Tim Cahill, Mikel Arteta and Marouane Fellaini.
"The thing with the league this year is that there have been so many times when we've thought we can push into the top half and make inroads into the top seven and we've always faltered," said Neville.
"Now we're eighth and the way it's going this year anything can happen. We've just got to finish as high as possible. There are eight games left and I don't think one team from that middle section have put a run together yet.
"We aim to be above Bolton, Sunderland and Liverpool. If we finish in front of Liverpool and don't achieve anything, that's still a failure for me."
Source: PA
Source: PA