An article in the Sydney Morning Herald claims the 21 year old centre has been offered a contract that would three times the value of his current deal with Waratahs.
The younger Tuipulotu has previously spoken about his ambition to play for Australia and said he had no plans to join his brother in Scotland but the attractive financial offer, and being behind Test-capped centres Lalakai Foketi and Izaia Perese at Waratahs, may be enough to prompt a rethink.
Scotland head coach Gregor Townsend also confirmed he had been in touch with Mosese, to encourage the Australian-born centre to join his brother at Glasgow Warriors when his contract with the Waratahs runs out at the end of the current Super Rugby season.
"I was asked by Glasgow to have a chat with him," Townsend confirmed to The Offside Line. "I actually had a chat with him two years ago by mistake, because Sione had given his old mobile to him, and I phoned to chat to Sione and got him instead. So, we had a joke about that!
"He's a player who is interesting one of the pro teams, and us in Scotland. Sione's had such a great impact at Glasgow and with Scottish rugby, it's wise of Scottish Rugby to follow up on someone of real potential.
"He's a young player who has come back from a long absence with a knee injury, but he's started the season really well for the Waratahs Academy and I think he's in the 23 tomorrow for the game against the Hurricanes."
Indeed, Tuipulotu - who picked up a knee injury in the process - did make his Super Rugby debut from the bench in Waratahs' 34-17 loss to the Hurricanes in Wellington on Friday night.
Waratahs coach Darren Coleman said he expected a decision "pretty soon" on Tuipulotu's future, and revealed the simple question he asked the Melbourne-raised back.
"I didn't pitch to him, I asked him what he wanted to do with his footy," Coleman said in the Sydney Morning Herald.
"If playing for Scotland and living in Edinburgh or Glasgow is what he wants to do, then he should go for it. I don't begrudge anyone making decisions for themselves.
"If being a Wallaby and being in a top Super Rugby franchise and really cementing yourself in that is what you want to do, then stay with us."