Barkley, whose spell with Everton fell away due to a hamstring injury in the first half of the current campaign, has received praise from new manager Conte ahead of his new challenge with with the Blues.
Chelsea, who face Arsenal in the EFL Cup on Wednesday before meeting Leicester City on Saturday, have been backed as the ideal destination for England international Barkley to progress.
"We have five months to show he deserves a call with the national team for the World Cup," Conte told Sky Sports News. "I hope [he gets one], because it means he will do very well with us."
"It's important for me to see him, to understand his physical condition," the Italian added when asked about a timescale for the midfielder's return to full fitness. "My hope is to have this player [available] very quickly.
"He can play in midfield, if we play with three midfielders, or number 10 if we play 3-4-3. Before playing we must be sure that he is into our idea of football. Otherwise, it's a problem for him and it's a problem for the rest of the team."
Conte's team will be looking to gain a considerable advantage over London rivals Arsenal in Wednesday's meeting.