Mark Warburton brought the pair to Ibrox club Glasgow Rangers last summer.
The 24-year-old defender is contracted to the Gers until 2018 but he and striker Martyn Waghorn - both signed from English clubs last summer - have rejected the extensions forwarded by Rangers, according to The Daily Mail.
The duo played starring roles in helping the club dominate the Scottish Championship last season en route to sealing their return to the Premiership for the first time in four years.
That being said, Tavernier has rejected the notion that he is unhappy with Rangers, insisting that both he and Waghorn are loving life in Glasgow and reveals that his contract situation will be sorted shortly.
“I don’t really read the papers, I’m fully committed to Rangers,” Tavernier said via The Glasgow Evening Times. “Me and my family love it here and I know that Waggy and his family absolutely love it up in Glasgow too.
“We see our futures at Glasgow Rangers, and I’m sure it will get sorted out soon. It’s just normal contract negotiations. This happens up and down the country no matter what club you’re at."
Both men scored in the 2-0 League Cup win over Motherwell on Saturday as Mark Warburton's troops kicked off the new season with victory.