The singer has barely spoken to his older brother Noel Gallagher since the guitarist walked out on the super-group after the pair had a pre-gig bust-up in August 2009.
Debbie - who previously acted as manager for Liam's new band Beady Eye - has now come up with a proposal for the band to do three concerts in 2014 to mark the 20-year anniversary of Oasis' acclaimed debut album 'Definitely Maybe' and is using the pair's other brother Paul to try and get Liam, 41, and Noel, 46, to make peace.
A source told the Daily Mirror newspaper: ''Debbie is working hard to bring back Oasis by regularly negotiating between the brothers. She gets on well with Paul and he's keen to bring his family back together.
''Debbie is helping Liam with his career and feels a reunion, with three dates in surprise venues, is a workable target. Liam trusts her implicitly and has agreed to seriously consider it.''
Liam and Debbie, 31, have been living together for the past few months, following the demise of his marriage to Nicole Appleton, which ended acrimoniously after it was revealed the 'Wonderwall' singer had fathered a love child with American journalist Liza Ghorbani.
The wild rocker is currently locked in a legal battle with Liza, 39, who is demanding financial support for their 10-month-old daughter Gemma as well as full custody.
Divorce proceedings between Liam and 38-year-old Nicole - with whom he has 12-year-old son Gene - have also begun with the rock 'n' roll legend hiring Fiona Shackleton to represent him as he looks to protect his estimated £40 million fortune.
Shackleton represented Sir Paul McCartney in his bitter divorce battle with Heather Mills.
Noel recently dismissed suggestions Oasis could reunite in 2014, insisting he'd only rejoin his brother if he was broke.
The songwriter - who has enjoyed a successful solo career since quitting the band - said: ''Maybe people keep thinking if they say it, it will eventually happen. It's not going to happen. Unless they're doing it without me, but without me it would be rubbish. One can never say never, because one might be skint. But I've got no intention. I'm not interested.''
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Pratchett died aged 66 in March 2015.