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The newspaper claims that Rangers top scout John Brown watched the duo last week and the Gers are now set to make contact over potential loan moves.
It is understood that Scottish side will take the pair to Ibrox to give them regular first-team experience.
McTominay has played four matches at senior level for United so far this season, including twice in the Champions League.
The 20-year-old has had an opportunity to play under Jose Mourinho, but the report states the Red Devils will now ponder his future as some senior stars return from injury.
Meanwhile, 19-year-old Hamilton is yet to register any senior appearance for Man United, but is regarded as a highly-rated talent from the academy.
Scott McTominay and Ethan Hamilton good move for Rangers?
Rangers could do with some new players and bringing in some loanees from Manchester United could be a smart move.
The Gers are still yet to appoint a new full-time manager and on the hunt for a new manager for the second time this year after Pedro Caixinha’s turbulent tenure was unsurprisingly brought to an end earlier last month.
McTominay has impressed so far for United’s first team and is a composed central midfielder that made a huge step up on the Champions League stage.
McTominay is technically gifted, composed in possession and would be able to strengthen Rangers in the middle of the park.
Hamilton on the other side, is more of an unknown quantity, but it is worth taking a punt on the central midfielder.
Likely to happen?
It seems like the Scottish giants could well be in with a chance of signing the midfielders, especially if they pursue academy star Hamilton.
The Gers currently have Ryan Jack and Jason Holt in the middle of the flank, while Graham Dorrans is currently out of action with an ankle injury.
Rangers are going to need new signings in the January window and building up a good rapport with the Premier League club would work in their favour at helping nurture their youngsters.