The Light Blue legions have travelled in huge numbers as the Ibrox side won the Third Division and League One titles in the past two seasons.
Clubs in the second tier will now reap the rewards of the Gers away support, and the addition of Edinburgh clubs Hearts and Hibs will ensure the Championship will be the most interesting and exciting league in Scotland next term.
Livi boss McGlynn said: "We've really got to use this as much as we possibly can. In terms of location, we're perfect.
"As soon as Rangers ended up in the bottom division [two years ago], it was forecast they'd be in the Championship in a couple of years.
"The financial situation at Hearts put them into administration and, as a result, they find themselves in this league.
"Once they were hit with a 15-point penalty, you're thinking it could be Hearts and Rangers in this league. The bonus ball nobody would have expected, was for Hibs to be relegated.
"We are looking for big crowds. The fact we have a 10,000-seater stadium means we can get plenty fans in.
"Rangers, Hearts and Hibs carry big travelling supports and we have a stadium that can accommodate that.
"Having these teams visit us will bring some great occasions and we're looking forward to them."
Dundee United youth chief Stevie Campbell reckons the Arabs have pulled off a signing coup with the capture of Rangers youngster Charlie Telfer.
The midfielder turned down a new deal at Ibrox to join Jackie McNamara's side this week, with compensation now to be agreed between the clubs.
Campbell said: "It's a big compliment to everyone that works within the club. People know that there is a pathway into Jackie's first team.
"I've got to commend him for that because he's shown bravery in throwing the young players in. For the likes of myself and everyone connected with the youth set-up it's a boost.
"Telfer is very much an attacking midfield player, he's got a fantastic touch, awareness and range of passing.
"He's a clever, clever player and I would like to think we've got quite a few of them within our squad."