The Rangers veteran striker hopes Mark Warburton can bring the experienced midfielder to Ibrox next season.
Reports in the past week or so have suggested that the Gers will offer the 33-year-old midfielder a two-year contract to move north of the border and become a key man in their return to the Scottish Premiership.
Though Barton's career has been one often dogged by controversy and questions over his discipline, the Burnley man, who is out of contract next month, would bring a wealth of experience to Ibrox, having won three promotions from the Championship, starred in the Premier League, spent a year in the French top flight, and played for England at senior level.
Former Gers midfielder Ronald De Boer said earlier this week that Barton can be the leader in the midfield that the club will need when they return to the top flight, and Miller appears to be of the same opinion.
The 36-year-old, who has played 226 games for Rangers and has scored 20 goals in 42 appearances this season, believes the signing of Barton would be a huge statement as they look to return to challenging arch-rivals Celtic next term.
Miller told Sky Sports: "It's no secret that the club are trying to persuade him to come to the club and hopefully we've done enough. The manager has never talked down the size of the job here and the size of the club so it would be a big thing if we could bring a player of that quality to this football club.
"He's at the stage of his career where he has the potential to play Premier League football and if we can get that signing over the line, it would be a massive coup for the club.
"He seemed genuinely interested and keen to know what the club was about. He knows the size of Rangers but he seemed interested in the subtle things about the club too."
Whilst Barton is thought to have offers from other clubs, one key advantage that Rangers could boast over their rivals for his signature is that they will be able to offer the prospect of Europa League football if they can beat Hibernian in next weekend's Scottish Cup final.
Barton is considering his options and is likely to make a decision on his future next week.