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Conte met with Levy, the Spurs chairman, and managing director Paratici on Monday to deliver his assessment of the squad and discuss January targets.
It is understood the trio agreed to prioritise signing a new right wing-back – with Wolves’ Adama Traore their leading target –, midfielder and forward this month, while a number of fringe players will be made available for transfer.
Conte repeatedly described Spurs as "in the middle" in a damning assessment of the squad’s level after last week’s 2-0 defeat to Chelsea in the Carabao Cup semi-final first leg, and his evaluation of his players is likely to have made for uncomfortable listening for Levy.
Matt Doherty, Tanguy Ndombele, Dele Alli and Joe Rodon are among the players who could leave on loan or permanently this month, although Conte has suggested he wants to keep Steven Bergwijn, the subject of a failed bid by Ajax, and Harry Winks.
Asked for details of Monday’s meeting, Conte insisted he had not tried to be "too soft" or "polite" with Levy and Paratici, but says he was satisfied with the outcome.
"It was a good meeting," Conte said ahead of Wednesday’s second leg against his former club.
"With Paratici, I have the possibility to speak every day but to have the possibility to speak with our owner [Levy] was important.
"I like to have this type of relationship, to be honest and to always tell the truth. You know I don’t like to tell a good lie to keep a good relationship or to show me very soft or to be too polite. It was good to tell the truth and it was a good meeting.
"Now for me it’s ok, I asked the club time to make my evaluation [of the squad]. The club asked after one month to have a meeting and I said no, I prefer to have another month to make the right evaluation. It’s honest, to give more time to me and also the players, to show me who deserves to stay here.
"Now the situation is very clear and I had this meeting, I was satisfied to have this conversation with the owner.
"Now I have only one way. It’s on the pitch and the training sessions every day. My only way to improve the situation is to improve the level of my players and this way the level of the team is going to rise. Then, the club know the situation and if they want to help me another way I appreciate it. Otherwise, I continue to work the way I am working."