It is being touted that his former club Newcastle United are interested in bringing him back to St James’s Park while Brighton, now in the Championship, have had a long-standing admiration for the attacking full-back.
However, as he seeks to exorcise the demons of Progres Niederkorn and advance in the Europa League, Tavernier seems like a man who is not in any hurry to depart.
He has just celebrated his fourth anniversary as a Rangers player and it would appear that he is planning many more.
The 27-year-old won the Championship and lost the Scottish Cup final in his first season, 2015-16. Winning a major honour is a priority.
He said: “The lack of silverware has been disappointing. The reason I came to Rangers was to win trophies.
“The squad has improved from last season, I’m more than excited to play in this campaign and hopefully we can bring silverware home this season.
“Being captain, winning a trophy would be the next step. I really wanted that as a player even more now as a captain. It’s been a long time coming – hopefully we can now do that.
“I have always believed in my quality, even when I was younger. With the clubs I was at, Newcastle and Wigan, it didn’t work out for me.
“Rangers gave me a chance. The club have shown faith in me. I have been trying to repay that favour ever since which means working harder, getting better and better.
“It’s a compliment to be linked to other clubs. I see it. But all my emphasis is on Rangers. Things can happen in football, of course, but I’m looking forward to this season.
“It’s all speculation. If it stays like that then I don’t get upset about it. I’m fully focused on the job here.
“I love my football here, my family is settled, I’m in a great place at the moment. Whatever happens, happens. I’m just focusing on Rangers.”
Tavernier was one of the men who remain culpable for arguably the worst European exit by a Scottish team when Rangers were embarrassed by Niederkorn two years ago. He is not anticipating a similar scenario as they face them tomorrow night at Ibrox and then next week at the scene of the crime in Luxembourg.
He said: “Ryan Jack and I were just talking about this the other day, it was Jacko’s first game for Rangers, and there are obviously some bad memories there.
“Looking back two years now, we didn’t take our chances at home in the first leg. We go over there, a goal goes in and the lads went under a little bit, and then we concede again.
“It was a bad night. That was my first time in Europe with Rangers and to get knocked out was awful.
“Seeing the reaction of Pedro Caixinha and the supporters – that’s when the defeat sunk in.
“There were a lot of mixed emotions right after the match. Rangers shouldn’t be knocked out of a European cup competition by Progres, with all due respect to them.
“Our fans want better than that, so did the players, and we need to put that in the past. I fully believe this team can do the job.
“Look, we had a good European campaign next season and we want it to do the same.
“I have the experience from last season. Obviously, the home tie is about taking your chances and being able to shut up shop which we did last season – against Maribor for example.”
“The squad is completely different, the gaffer is in now, and I’m sure we can find something. We’re not going to undermine them, we’ll take them very seriously and see if we can get the job done.
“The gaffer and Mark Allen have obviously taken the club forward massively. The training ground has been refurbished, that’s happened at Ibrox as well, the surroundings have improved which has made everything better for us as players. We have come a long way.
“The players who have come in have brought up the levels even higher. All the coaching staff are doing a tremendous job, the boys enjoying working with them, and the demands are even higher.”