At the end of July, we understand Tottenham made the first steps towards Liverpool over a potential deal.
Those initial enquiries were met with little encouragement, with the Reds showing little appetite to sanction Gakpo's departure.
But as we revealed, Liverpool were relaxed about Gakpo's future, and there was a sense they would entertain a sale if an offer was too good to turn down. It is starting to look like that moment could soon arrive.
Liverpool have been working towards a major deal for Paris Saint-Germain's Bradley Barcola, and Tottenham believe that if the Reds can get that move over the line, it will pave the way for Gakpo's departure.
The player has already intimated through intermediaries that he would be interested in joining Spurs, giving the club further encouragement as they explore the possibility of a deal.
Tottenham view Gakpo as more than a left-sided attacker. His ability to operate centrally is also seen as particularly valuable following the significant injury suffered by their main target, Eli Junior Kroupi.
Spurs are also looking to finally close a deal for Savinho.
Manchester City had been expected to receive around £70m for the Brazilian, although there has been some noise that Tottenham's eventual deal could even exceed that figure.
Gakpo is also likely to cost around £70m, but sources say it would be a total outlay that fits within Tottenham's financing for this transfer window.
We understand the club had promised Roberto De Zerbi that his new signings would be in place by the time the season begins. He is very keen on the addition of Gakpo, who has been made aware of the personal terms on offer.
With Brentford up next weekend, the clock is now ticking for Spurs to get their business done.