The former Wigan right-back is fast approaching double figures already.
The 73-year old – who spent his whole career at Rangers between 1961 and 1978, making 498 appearances in the process - was voted into the club’s Hall of Fame in 1999 and was known for his goalscoring exploits from defence.
The former Scotland international managed 87 goals over the course of his Rangers career and Tavernier spoke of his desire to beat one of Grieg’s records.
“I’m having a little bit of banter with John Greig,” said the 23-year old, in quotes published by the Daily Record.
“He says he scored 12 goals in a season once so I’m kind of after that record and beating him because we have good banter together.
“It’s a bonus if I score a goal. Obviously, I’m delighted when I do so but it’s all about helping the team.”
Tavernier has started the season in fantastic form and looks well on course to better Greig’s 12 goals, having notched his ninth of the season against Falkirk on Saturday.
The former Wigan man has been a revelation at Ibrox and has emerged as something of a free-kick specialist in his new surroundings.
Tavernier, along with fellow ex-Wigan man Martyn Waghorn, have been the standout signings for Mark Warburton and both look set to fire Rangers towards the top flight.