However the latest bid will see them get the cold shoulder from Lyon, who have made their valuation clear.
The Cameroonian international had something of a breakthrough year last term and can play anywhere across the front-line.
Mauricio Pochettino is keen on the player to add some pace to his attack.
It is now being reported in France that Spurs have launched a third bid for the player this week.
L’Equipe says the previous offers from Spurs have been rejected, but that the club carry on unperturbed.
The new offer is said to be worth €13 million, with a further €3 million in add-ons. That equates to an initial fee of £9.2 million and potential add-ons of £2.1 million, an overall package deal of around £11.3 million.
However, this deal will also be rejected, according to the report.
It is claimed that Lyon are beginning to come to terms with selling N’Jie, but only at the price they want.
That price is around €15 million (£10.6 million) with bonuses yet to be added on.
Lyon have not yet responded to the latest offer, with the report claiming they will not do so, as they have made Tottenham fully aware of their expectations.