The 32-year-old has earned legendary status during his nine-year stay at Rangers and has won five major domestic honours, including the 2020-21 Scottish Premiership title and last season's Scottish League Cup.
Tavernier, an attack-minded right-back, has scored an impressive 125 goals and provided 129 assists in 460 appearances for the Gers across all competitions, netting at least 18 goals in each of the last four seasons.
The Bradford-born defender still has two years remaining on his contract at Ibrox, but speculation over his long-term future has recently surfaced amid suggestions that he could be stripped of the captaincy by manager Philippe Clement.
Tavernier was appointed Rangers captain in 2018 by former Gers boss Gerrard, who is now keen to lure the Englishman to the Middle East.
According to Football Insider, Tavernier has accepted the 'astronomical' contract offer presented to him by Al Ettifaq, who finished sixth in the Saudi Pro League last season.
Tavernier's Rangers future uncertain amid Al Ettifaq offer
The report adds that the financial packages offered to Tavernier would 'massively' increase his wages from his current deal at Rangers.
Although personal terms have been agreed, it is understood that there is no agreement between Rangers and Al Ettifaq over a transfer fee just yet.
Nevertheless, it has been claimed that a deal for Tavernier to move to Saudi Arabia is 'increasingly likely' to be finalised between both parties.
The news was reported before Tavernier was chosen to front up the launch of Rangers' new home kit, which was unveiled on Thursday evening.
Should a transfer to Al Ettifaq materialise for Tavernier this summer, he would link up with the likes of Scotland international Jack Hendry, ex-Liverpool midfielder Georginio Wijnaldum and former Everton winger Demarai Gray.
Rangers have already been busy in the summer transfer window, recruiting a total of five players to date including their latest addition of goalkeeper Liam Kelly on a free transfer from Motherwell.