The Ibrox skipper has netted an incredible 13 goals so far this season from right-back with Gers unbeaten in all competitions.
Victory against Benfica could see Gers through to the Last 32 of the Europa League tomorrow night – but even despite the start both he and his team have made to the season, Tavernier is still targeting even further improvement.
He told today’s press conference: "I am really proud of the squad and I feel we are in a great place at the minute. We have worked extremely hard over the course of the season to get to where we are now.
"But we still have a long way to go. It's so far, so good, but we know we can still improve in areas and all the lads on the training pitch are willing to make that difference and to train really hard, so I am really proud of the boys.
"For myself, I'm just really enjoying my football. That is down to the lads I'm playing with and the squad we have got and the license the gaffer and the management team have given us in the games.
"I'm always still trying to look to improve myself, and hopefully that will continue."
Gers drew 3-3 with Benfica in Lisbon three weeks ago, and looking ahead to tomorrow’s meeting, Tavernier continued: "We still know it's going to be a tough game as Benfica will undoubtedly be favourites and one of the favourites to win the competition.
"We know it will be a very tough game and they have very good players, but I believe in my team and our capabilities.
"If we stick to the game plan the gaffer and the management team give us, and we apply that from the first minute, it should put ourselves in a good place.
"We have to try and be better defensively, and hopefully we can create chances to score goals."
Gers are now into a hectic schedule of games between now and New Year, but it’s a period Tavernier is relishing.
He added: "There is nothing better than playing as many games as possible as that is what you want to do as a footballer.
"The schedule coming up will be play a game, recover, play a game so all the boys are looking forward to it - it's part and parcel of playing games and I can't wait for the busy schedule.
"Normally it makes the weeks go quicker so I am looking forward to it."
WATCH THE FULL PRESS CONFERENCE WITH TAVERNIER BELOW