Speaking to Football Insider, Mills insisted the player’s experience would be invaluable at the club.
The Sun reported this month that the Gers are eyeing the veteran centre-half and have now offered him a £35,000 per week contract.
He is currently a free agent after his Crystal Palace deal expired at the end of June.
The Sun’s Tom Barclay reported few days ago he has rejected a new contract proposal from Palace as he’s holding out for higher wages.
Quizzed whether Cahill would be a good recruit for Rangers, Mills told Football Insider: “Definitely.
“He looks after himself, keeps himself fit. He’s solid, reliable and very, very experienced. He’s a good professional and I think that would be a top-quality signing.
“We all know that the standard of the Scottish Premiership is not the greatest in the world so in terms of quality it’s not a problem. It’s also what else he brings, that’s what’s really important.”
Cahill also has 61 England caps to his name and was part of the roster that reached the FIFA World Cup semi-finals three years ago.
Meantime, Wigan Athletic have declared their interest in landing Rangers wide man Jordan Jones, according to the latest reports.
The 26-year-old star has been told by the Ibrox management he is free to find a new club in spite of featuring in pre-season.
Jones would reportedly like to seal a permanent return south of the border after a stunning loan spell at Sunderland.
Wigan have been in touch over signing the versatile Northern Ireland international permanently.
Sunderland are also interested in converting Jones’ 2020-21 loan into a permanent one but his asking price is a major obstacle for them.
Rangers are said to be willing to let their player go for less than £1 million.
His 21 games at Sunderland in the second half of last term yielded three goals and four assists, although it wasn’t enough to secure promotion from the EFL League One.
Intriguingly, they begin their League One season on 7 August versus Wigan at the Stadium of Light.