The Ibrox captain started his career with the Toon Army, making a handful of appearances over a six-year spell.
The Premier League side, now under the management of Steve Bruce, are in desperate need of reinforcements even if they seem well stocked at right-back with Javier Manquillo and DeAndre Yedlin.
According to the Daily Mail, who broke the story, Rangers would listen to offers of around £8million for the 27-year-old.
The situation brings up the much deliberated issue of the value of players plying their trade in Scotland. It is a topic which has been discussed, written and argued about by fans both sides of the border in relation to Kieran Tierney and his protracted on-off move to Arsenal from Celtic.
The discourse around the Scotland international and his £25million price-tag opens up an avenue to analyse the value of Tavernier.
Back in March Rangers' managing director Stewart Robertson told fans at a convention in New Zealand that the club wanted as much as £20million for Alfredo Morelos.
The Ibrox side took the viewpoint that if Celtic sold Moussa Dembele to Lyon for just shy of the £20million mark, they should demand just as much for the Colombian. The value debated and disputed by many in Scottish football.
The idea that 'player A must be worth at least value X if player B was sold for value Y' is not an exact science.
It has been used in relation to Tierney and the £50million Manchester United parted with for Aaron Wan-Bissaka.
It is, of course, understandable. One has a glut of trophies to his name, played 170 times for one of the most demanding clubs in Europe and fared well on the international stage against the continent's elite. The other has made less than 50 appearances for Crystal Palace.
Yet, despite there being a just a year age difference there is a £25million disparity between the two, in favour of the latter.
Simply put, playing in the Premier League and being a highly-rated English defender adds a certain premium.
Returning to Tavernier. In terms of his importance to Rangers, it is actually something which can be quantified.
- Since joining in 2015 he has missed just 10 of Rangers' 208 games
- He has been absent for just three league games in that time. Rangers failed to win each time
- Last season he was the highest scoring full-back in world football (top flight, domestic cup and continental fixtures)
- Last season he was involved in more goals than any other defender in world football (top flight, domestic cup and continental fixtures)
- He has contributed to more than 100 goals in 198 appearances
- In the 2018-2019 Scottish Premiership: he topped the assist charts
- No player contributed to more goals
- Delivered most crosses (216) with a 40.74 per cent accuracy (9th best)
- Had 59 touches in the opposition box - the most for any defender
- Made the third most passes (behind Celtic duo) Callum McGregor and Scott Brown
- The most through passes (58), the most key passes (24), second for passes to the final third (369), most smart passes (41) alongside McGregor, progressive passes (502), second for oppressive runs (93) and second for deep completions (64).
Tavernier is an attacking tour de force. He is one of the most valuable players to his team in the country, more so than Tierney to Celtic.
There are times, when the going is getting tough, Rangers turn to their captain - a defender - to produce something special, to make that run or that cross.
There is no doubting he is a peculiar player. A full-back who acts like a winger with the added bonus of having that ability, usually reserved for strikers, of being in the right place at the right time in the box.
It has to be noted that his goalscoring figures have been swelled by penalties but there is no other full-back in the country so adept at getting into goalscoring or dangerous positions as Tavernier.
There has, however, always been one large, invisible question-mark-followed-by-exclamation-mark hanging above his head when he plays. 'But can he defend?!'
Arriving under Mark Warburton in the Championship Tavernier was constantly on the front foot. As is the case with attacking full-backs, there is a suspicion that they have vulnerabilities when defending.
With the Rangers captain used as a key attacking component, he is going to find himself in situations where he is out of position or has left acres of space behind him.
If he is being asked to get forward into the positions which see him impact the game in the final third, that is on the manager to alter the team to cover for the player.
The bigger issue is when Tavernier is faced with a defensive duels or a one-v-one situation. In terms of success rate for the former, in the previous season he recorded just shy of 70 per cent, compared to Tierney's 76.19 per cent. But there have been big improvements for the Rangers star since arriving, as he has developed into a much more rounded and refined defender.
Rangers will never get near the £25million Tierney is rightly valued at. The Scotland international is proven on the European stage and has a much higher ceiling in terms of potential. And, without beating about he bush, is a better player.
However, the £8million quoted for Tavernier looks on the cheap side.
With Gerrard having put together his side for the coming season - one more signing is likely - losing Tavernier would be a huge blow. Not only would the side be losing their captain but it would prove very difficult to replicate his qualities with another signing.
It would be remiss to label him priceless. But in terms of what he adds to Rangers the club would realistically want more than £8million for a player who, across 198 games for the club, has proven himself to be so valuable.