It is believed both Everton and Chelsea would rather settle Barkley’s future before the final days of the January transfer window after the saga ran the length of the summer.
Other than Barkley, Chelsea are interested in Monaco’s Thomas Lemar, although the Ligue 1 club have insisted that the France international will stay put until the summer.
Conte wants to strengthen the left side of his squad and remains a big fan of Juventus wantaway full-back Alex Sandro, who is also on Manchester United’s radar, while Chelsea continue to be linked with Porto’s Alex Telles.
Chelsea had been interested in Virgil van Dijk and asked whether the Dutchman’s £75million move to Liverpool makes his own task even harder, Conte said: “It doesn’t change. For us, I repeat, it’s very important to look at ourselves and then try to find the right way to improve.
“On my hand, the way to improve this team is to work. On the other hand, there is the club and the transfer market.
“But I can only speak about my hand. I see now only one way to improve my team – to continue to work with this mentality, this desire, this will. Because, I repeat, I can tell you I have fantastic players with me.
“The transfer market – this window – could be important if we are able to find the right players. Otherwise, we continue to work with these players.”