Daniel Levy has been sent a January transfer window warning, which will become even more important if the deal with Luis Diaz fails.
football.london reported Tottenham's interest in Diaz on Tuesday but later in the day it was revealed that the Lilywhites had had a £37.6million offer rejected.
The 25-year-old has a £66million release clause in his contract with current club Porto, so an offer will need to be closer to that price to secure the deal, which could make it less likely.
Spurs have been linked with various other players during the window including Adama Traore and Franck Kessie, but are yet to bring any players to N17, 26 days after the transfer window opened.
The defeat at Stamford Bridge on Sunday was a further indication of the gap in quality between Tottenham and the likes of Chelsea, Liverpool and Man City.
Conte has already explained that this won't be solved in one window but the final week ahead of the winter window deadline day is a good place to start.
With the likes of Giovani Lo Celso, Tanguy Ndombele and Dele Alli all being linked with a move away from Spurs, the Italian would then become light on attacking players for the middle of the field - which is where Diaz could come in.
However, if Tottenham fail to come to an agreement with Porto and the Colombian, it won't leave much time to get other fresh faces in.
Former Spurs players, Paul Robinson and Jermaine Jenas have both had their say on the transfer window for the north London club.
"The thing that frustrates me with Tottenham is that they always wait until the end of January and Tottenham notoriously do that more so than any other club," Robinson said ahead of the scheduled North London Derby, when speaking to BetfredTV.
"They need to back the manager. They need to change and there are players that need to leave and will leave. Don’t wait until the end of the month just so you can save yourself a few quid."
Levy and Fabio Paratici have already waited until the end of the window to get business done, which is often the case at Spurs.
"Antonio Conte is going to want to put his own stamp on the team. They haven’t won a trophy and the squad’s not good enough," Robinson added.
"They’ve now got a world class manager so they’ve got to give him the funds, support him and give him two transfer windows to do it."
Jenas echoed the ex-Spurs goalkeeper's point in regards to the Italian being a world class manager but needing the backing to create success for the Lilywhites.
"When it comes to who is the right manager for Tottenham right now, all of my belief is in Antonio Conte - and I honestly think I can speak on behalf of most Spurs fans when I say that," Jenas said in his analysis on BBC after the Chelsea clash.
"I genuinely believe he is building something but, to do it, he needs the right players - and I have never seen the point of hiring Conte if you are not going to give him what he needs.
"It would be stupid for Tottenham chairman Daniel Levy not to back him, because Conte is the one," the 38-year-old admitted. "He is the guy that Levy should want at his club for the next five years, so he has got to treat him accordingly.
"I feel the same way - backing Conte and giving him what he needs to challenge for the top positions should not be seen a gamble. Why wouldn't you help him?"
There is a strong understanding that incomings are needed to help improve the Spurs squad and fans will hope that some business can be done in the final week of the window.
