The Red Devils fell 14 points adrift of rivals and defending champions Manchester City this weekend after being held to a goalless draw by struggling Crystal Palace.
Mourinhos side have won less than half of their Premier League fixtures to drop to seventh in the table. They have also endured mixed results in Europe.
Wales manager Giggs won a staggering 13 league titles during his 24-year spell at Old Trafford and says sacking Mourinho is not the answer.
'Sacking Jose will not change anything' – Giggs
I dont see why changing the manager at this stage will change anything.
Everyone knows what a successful manager hes been over the years. I believe that bit of stability weve not had over the years – we need to stick with him.
But results also need to change. I think weve got the manager, the players to do that.
Manchester City and Liverpool, the teams up there, they are consistent. When youre not the gap is obviously going to be big.
When your nearest rivals are that far ahead of you its hard to take. Its still 13 games into the season, time to claw it back.
But the only way of doing that is going on a run of seven or eight games unbeaten – small steps to build that confidence back up.
Neville, also speaking to Sky Sports, says Mourinho is likely struggling with his team selection after a poor start to the campaign.
The former England defender praised Mourinho for asserting that Manchester United would finish in the top four before the Crystal Palace fixture.
But he claims Uniteds inconsistency is the main reason they are not title contenders.
'Man Utd are not right at the moment' – Neville
I didnt go to Old Trafford but I spoke to people who did. Theres a lethargy, in terms of the fans going into the ground, watching the game, players on the pitch.
I think Jose gave the right message before the game saying they will end up in the top four.
I dont think it would have been acceptable at the start of the season, and certainly the start of last season, to say the top four is achievable, because he will have wanted to challenge for the title with the money that has been spent. Thats where United need to be.
But theyre not near that level at this moment in time. Theyre inconsistent, not just in games, but from half to half within games.
Its not right obviously at this moment in time, the players are not performing anywhere near their level.
Youd argue Jose at this moment in time will be scratching his head about which players to put out on the pitch.
But hes made changes before and it hasnt really made any difference so its just about battling and fighting away at it, because it is a struggle. I think thats the word to describe it.