Gordon has twice led the side in the absence of Redpath, in the World Cup warm-up defeat to Ireland and the 39-15 win over US Eagles nine days ago.
"It was an awesome experience to carry the ball onto the field in front of a packed crowd at the World Cup," he reflected.
"I had been captain against Ireland, but we didn't get the result we wanted, so the USA match was the kind of night you dream about.
"As a young player you always just dream of playing for your country, but once you get into the team you start to think 'hey, maybe I could captain these guys'. I've had a taste of it now and it would be nice to be considered when Bryan steps down.
"There will be a new coach coming in who will have new ideas, and I am sure he will look at all the personnel in front of him," he added. "But hopefully I will be in with a good shout."
Scotland team to play Fiji at Aussie Stadium on Saturday, November 1: G Metcalfe (Glasgow), S Danielli (Bath), G Townsend (Borders), A Henderson (Glasgow), K Logan (Wasps), C Paterson (Edinburgh), B Redpath (Sale), T Smith (Northampton), G Bulloch (Glasgow), B Douglas (Borders), N Hines (Edinburgh), S Grimes (Newcastle), R Beattie (Gwent Dragons), C Mather (Glasgow), S Taylor (Edinburgh).
Replacements R Russell (Saracens), G McIlwham (Munster), J White (Sale), J Petrie (Glasgow), M Blair (Edinburgh), J McLaren (Aviron Bayonnais), B Hinshelwood (Worcester)