The one transfer lesson Chelsea will never learn amid fresh links with ex-Real Madrid star Karim Benzema

Jordan Henderson has gone, and others will likely follow – many players and coaches who took up the offer of extreme wealth in Saudi Arabia have discovered that their decision was not a good one. And if the rumours that have swirled around Riyadh for the past couple of weeks are at all accurate, legendary striker Karim Benzema could be the next star to flicker out of the Saudi constellation.

Chelsea, Arsenal, Manchester United and boyhood club Lyon have all come up as possible destinations for the 36-year-old, who has found the hero worship he might have expected from Saudi Pro League supporters to be in short supply. He has scored 12 goals in 20 games for new club Al-Ittihad, but has also come under heavy criticism from the stands and in the media for lifeless displays. More recently, he was reportedly excluded from his side’s training camp after reporting late from a holiday in Mauritius.

Benzema has been keen to downplay the rumours, describing claims in the French media that he wants to leave Saudi Arabia as “completely false”, but his representatives appear to be working to secure a move nonetheless.

Lyon, a fallen French giant struggling to retain their place in the French top flight, are the most romantic and perhaps most likely destination for a man who has won just almost everything at club level – but Chelsea’s name has cropped up quite a lot, and they are certainly in the market for a new striker. But would a move to Stamford Bridge make sense for Mauricio Pochettino’s side?

Chelsea have been here before – they signed several ageing greats up front through the Roman Abramovich years and few succeeded. Samuel Eto’o, Fernando Torres, Andriy Shevchenko, Radamel Falcao, Gonzalo Higuain, Pierre-Emerick Aubameyang and even Didier Drogba, in his second spell at the club, were all bought based on past glories but were unable to recreate them.

In some cases, it was age, in other injuries that left the players as supercars with broken engines. In one or two cases, it may have been the case that players who have achieved all that they wanted simply couldn’t muster up the energy and drive needed to continue to be greats at the top level. Benzema may well be in the latter camp.

There are no publicly-known issues with his fitness, bar a couple of games missed in December thanks to a back problem. Nor is there any suggestion that he is no longer capable of playing at the top level, given that he scored 31 goals in 43 games for Real Madrid just last season. But if the drive is no longer there, then he would likely be no more than another once-brilliant forward who couldn’t do it at the Bridge.

If the drive really was still there, if there was still a hunger to achieve more, one wonders if he would have left Madrid in the first place. Perhaps he really did buy into the idea of starting something special in the Saudi Pro League, but more likely his move was motivated by money alone. Most players who have headed to Saudi Arabia for this first page of a wildly expensive project are doing so for strictly mercenary reasons, after all, and certainly nobody is going there for the glory. Perhaps in a decade or two’s time the Saudi Pro League title will be as significant as silverware in Europe’s traditional major leagues, but it is not there yet.

His performances have also implied a man who doesn’t have the will to be the best any more. 12 goals is no mean return in itself, but most have come against much weaker sides – a hat-trick against second-bottom Abha, who lack a star-studded squad of their own, is no great achievement. Only one of his goals has come against another member of the newly-minted Big Four of Saudi football. By way of a point of a comparison, his team-mate, unheralded 33-year-old Moroccan forward Abderrazak Hamdallah, has scored 15 goals in as many games.

Local sports journalist Walid Al-Faraj may have put it most succinctly: “The gap between Benzema and the public is growing day by day. He never managed to make a difference. And above all, he doesn't make any effort... Benzema has offered nothing."

And if he has offered nothing at Al-Ittihad, why would it be any different at Chelsea? If he won’t bust a gut for a reported €100m (£85.5m) per season, what would be his motivation under Pochettino? The chance to scrape Chelsea into the Europa League group stages? The EFL Cup final? Perhaps the backdrop of the Premier League would reignite the fire, but it’s all too easy to see a feeble flame sputtering out instead.

In any case, none of this is proof that Benzema is suddenly washed out or past his prime. He is only eight months or so removed from some remarkable form at the very highest level of the game, and there are no indicators that his body is giving up on him and preventing him from playing at his best, as was the case with Torres, for example, or Alexandre Pato.

Perhaps Benzema still has plenty to offer. Maybe he really is the short-term answer they need up front while Nicolas Jackson adjusts and develops and as Christopher Nkunku finds his form after injury. Or, perhaps, history would simply repeat itself, and once again Chelsea would find themselves hamstrung by an underperforming striker.

One day, Chelsea will find a consistent, first-rate number nine and solve a problem that has existed to a greater or lesser extent since Didier Drogba left for the first time. That isn’t likely to be Benzema – but he could be an exceptionally good sticking plaster over the cut. Or, perhaps, just leave it to Lyon to find out whether he’s still got it.