The former Oasis songwriter recently launched a tirade at Neville on Twitter after the former Manchester United and England defender tweeted the lyrics of Noel's classic track Fade Away.
But Gallagher has claimed he is a big fan of Neville's and hopes to make an appearance as a pundit himself.
Career change: Gary Neville (left) has moved into punditry after retiring
In an interview with Sky Sports, he said: 'D'you know what? I'm not being sarcastic here. I like him. I have always liked him. He is like the pantomime villain for City fans.
'I have always given him a bit of stick and he gives me a bit of stick. That's great. I've never met him, but I'm told by his mates that he's quite funny.
'I like him as a pundit and I'll tell you why, because he has only just finished playing and his words carry more weight than the likes of Alan Shearer or Alan Hansen or Andy Gray or any of that lot.
'When Neville was going on about Aguero's second goal and was saying how difficult it was, he would know. He has trained with (Cristiano) Ronaldo. He has worked under (Sir Alex) Ferguson.
'He has played with Rooney. He has played for England. He should have captained England, actually, he missed his calling. Neville looked quite uncomfortable when he was stood up on TV, but I like him. He'll get better at it and I congratulate him.'
True Blue: Noel Gallagher is a diehard Manchester City fan
Noel has released his debut solo single but fancies himself to follow in Neville's footsteps.
He added: 'I hereby throw my hat in the ring. I would love to sit in between Tommo (Phil Thompson) and particularly (Paul) Merson, because he hates City. I would love to sit next to Merson and flick him on the ear every now and again.'
On his own club's fortunes this season, Noel is excited about Sergio Aguero's arrival at City, and expects Carlos Tevez to stay put.
'I'm not sure about him [Aguero], you know... He might take a while to settle in... I was excited about the season anywaybefore I even saw him play.
'Even if we hadn't have bought him, I would still have been looking forward to a very exciting season, because I think we're very close.
'But, saying that, to play like he did on Monday,when he's supposedly not very fit, is a statement. It's great. It's money well spent already. We paid ?38million, he is already worth ?40m. Not a bad investment.
Instant success: Sergio Aguero hit the ground running on his City debut
'Well, you know, not that I'm a spokesperson for anyone, but I've been telling anybody that was going to listen that he's [Tevez] not going anywhere. He has been for sale since January, effectively, and if anyone was going to buy him, they would have by now.
'The season has started. They're not just suddenly going to stump up ?50m on a Saturday night. The good thing about Tevez, you know he can't give anything less than 100 per cent when he's playing. Even if he gives 75 per cent, that's pretty much more than other players' 100 per cent.
'He's still an absolute legend. If he doesn't like Manchester, fine. At least he has been very open and honest. He hasn't been snidey about it. He's saying he wants to leave, and that's fine. The club have said he can leave for this amount of money and everybody's cards are on the table.
'If nobody buys him, he's not going anywhere. So, he's still my mate. I still love him. I'll still cheer himwhen he walks out on the pitch, no question. I think most City fans will. I don't think his name will get booed, no way.'
Staying put? Carlos Tevez (centre) could remain at City despite his desire to quit
With Samir Nasri set to join City before the transfer window closes, Noel believes he will be an excellent addition.
'I think it (signing Nasri) is a brilliant move, because, with the Champions League, there are big chunks of the season when you're playing Sunday-Wednesday-Sunday.
'I think it's a greatmove for him and a brilliant buy for us. If he (Roberto Mancini) is going all out for steamrolling teams, he can play Silva and Nasri. If I was Gareth Barry, I'd be a bit worried!'
Despite being starved of success as a City fan until this year, Noel is glad he wears blue, and not red.
'My parents are Irish and, being Irish, we have about 108 cousins. They're all, to a man, Man United fans apart from me, our Liam, and our Paul (eldest Gallagher brother).
Success at last: City won their first trophy for 35 years last season
'My dad, this used to happen a lot in the Sixties and Seventies, used to go and see City and United in Manchester. He took us to my first game, which was City against Newcastle in 1974. Of course, you go into school the next day and once your allegiance is declared, that's it. The end.
'Luckily my dad never took us to Old Trafford. He took us to Maine Road. For years I resented it. When United were winning Trebles and the Champions League, I was thinking, "Why!? Why did he do that?". Then, Sheikh took over and I was like, "Thank the Lord. I knew one day my faith would be repaid".'
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Source: Daily Mail
Source: Daily Mail