The Gers defender had not even considered the possibility of competing on a continental front after just a single year at Ibrox.
Rangers defender James Tavernier has told the club's official website that he had not even considered the possibility that he might get a chance to play European football for the side when he joined last summer.
The Gers have already won the Scottish Championship - sealing promotion back to the top flight after a four-year absence - and the Petrofac Challenge Cup in the right-back's first campaign at Ibrox.
If they can complete a domestic treble next weekend by beating fellow second-tier side Hibernian in the Scottish Cup final at Hampden Park, they will secure a spot in the second qualifying round of next season's Europa League.
Tavernier admitted to the club's official website that the thought of competing in Europe in a blue shirt had not even entered his thoughts when deciding to move north of the border last summer.
The 24-year-old said: "When I first came up here, our objective was to win the league. But getting to the [cup] final, and the way we got to the final, is a great credit to all the staff.
"Having the prize of Europe at the end is something I would never have thought about when I came up here.
"Rangers are a massive club and I needed games, and with the ambition and the possibility to take the club back to where we needed to be, it didn’t have to be sold to me."
Tavernier has been a key player for the Gers in his first season in Glasgow, making 49 appearances in all competitions and scoring a remarkable 15 goals from right-back.
The former Newcastle United and Wigan Athletic has established himself as the unquestionably first choice in his position under Warburton and is likely to remain so in the Scottish Premiership next term.