The former Oasis stars have been at loggerheads ever since the band split in 2009, following a backstage fight between the pair.
And the siblings' feud was taken up a level in June, when a war of words on social media was sparked when Noel shared a threatening message Liam had sent about Sara to the guitarist's 19-year-old daughter Anais, telling his niece to warn her stepmother to be ''very careful'' after she mocked the former Oasis frontman ahead of his performance at Glastonbury Festival.
Liam, 47, has now given Noel, 53, the chance to settle their differences once and for all, but admitted he doesn't think his spouse will allow them to.
The 'Wall of Glass' hitmaker tweeted: ''We all have the ability to forgive n forget you've just got to want to and we all know your desperate to hang out with your little bro it's just your Mrs won't let ya oh well as you were LG x (sic)''
The younger Gallagher brother has been very vocal about his dislike for Sara in the last few years and he has cited her as a major contributing factor to the break-up of Oasis branding her a ''witch'' on numerous occasions.
Liam also once again referred to Noel's comments at the height of Oasis' Britpop feud with Blur, in which he stated, ''I hate that Alex (James) and Damon (Albarn). I hope they catch AIDS and die'', and accused Noel of being ''full of s***t''.
The 'Shockwave' singer wrote: ''Whatever I said surely wasn't as bad as what you said about Damon and Alex. Remember when you wished they catch AIDS and die. You're full of s**t Rkid you just ain't got it anymore. Bon voyage LG x. (sic)''
The 'One of Us' hitmaker's latest comments on Twitter come as Noel said he has no desire to reunite Oasis and will not being answering any invitations to his brother's upcoming wedding to Debbie Gwyther.
He has also joked about how he plans to spend the money when he sells the rights to Oasis' back catalogue, two months after he revealed that the masters to the 'Wonderwall' band's music is ''due to come back around to [him] in about four or five years''.
Speaking at the BMI London Awards, Noel quipped to BANG Showbiz: ''I'm getting rid of them (the rights to my songs) so I can buy a f***ing yacht and a chimp. Just to p*** off the eco-f***ing warriors. I'm going to buy two Lear jets, one for each personality I've got.''
Despite a reunion of the 'Slide Away' group not looking likely, Noel admitted he can't deny Oasis was the ''best band of an era'', but admitted they ''wouldn't'' be able to ''survive'' in the music industry now.
He said this week: ''There's always an anniversary coming up in the music business. There'll be on tomorrow morning of Bonehead's (Oasis guitarist) hair falling out or something.
''When I eventually die at the age of 104 and cryogenically freeze this hairdo, the newsreels will say ex-Oasis.
''I'm not bothered about my solo career compared to that.
''Nothing's gonna compare to that, we were the best band of our era by a f***ing mile. We were the best band in the world for about a year and a half.
''You only read about half of what we got up to. We wouldn't survive in this climate. I gave 20 years to the band, now I'm doing this for me.''
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