The former Liverpool right-back signed a two-year deal on Thursday afternoon to become the seventh summer addition under new boss Steven Gerrard.
This has fuelled speculation that Rangers are looking to depart with Tavernier, their first choice right-back in each of the past three seasons.
There have even been reports that Rangers are shopping the former Wigan Athletic defender for a fee of around £3.5million as they look to generate funds to improve the rest of the squad.
However, new No.2 Gary McAllister insists there are no plans to part with Tavernier.
He told the Scottish Sun: “In this period where Rangers have taken a bit of criticism, James has been one of the stand-out players and he is going to be key for us.”