Lanzini has been excellent over the last few years for the Hammers, so it is no surprise that some of the top sides in the Premier League are interested, with Everton also being credited with a recent interest in the Spurs target.
With Tottenham flying high in the Premier League and Champions League, while David Moyes will be looking to get the Irons out of the relegation zone in the top flight once the domestic season resumes, Lanzini would certainly be forgiven for considering his options if Pochettino did offer him the chance to move.
Therefore, West Ham need to be proactive before the January window opens and offer Lanzini the kind of contract that a player of his calibre could get elsewhere.
The Mirror reports that Lanzini earns £35,000 a week at the London Stadium. And while it is not clear what West Ham's budget is, the Daily Star reported in May that the Irons were prepared to hand summer target Ross Barkley a contract worth £140,000 a week.
While such a pay rise would be incredibly steep, it shows that the Hammers should have the funds to pay their talisman a lot more than they currently do.
Given Tottenham's current position, they would surely be able to offer Lanzini a significantly better contract than the one that he currently has - and with Spurs doing so well, the 24-year-old would be forgiven for finding it difficult to come up with a reason to stay at West Ham if they do not put fresh terms on the table.
And if offering fresh terms is what it takes to convince Lanzini to ignore Spurs' interest and stay with West Ham, the Hammers can have no excuse not to act as soon as possible.