The 24-year-old is expected to have a medical with the London club on Friday prior to completing a £15m move.
When asked about the deal, Conte told reporters Barkley was a “good prospect” but warned he was recovering from hamstring surgery in August.
“He’s very young and has a lot of space for improvement,” said Conte. “He is very strong, good technique.”
The Chelsea boss added: “He’s a good prospect but at the same time, it will be very important to understand, if the player signs, we must have patience to help him recover.
“Don’t forget he had a bad injury, a surgery and this player has not played for seven months.”
Barkley had hamstring surgery in August, the same month in which he turned down a move to Chelsea on transfer deadline day.
The England international rejected a new deal at Everton and is out of contract at the end of this season, opening the door for a cut-price move.
Everton manager Sam Allardyce said on Thursday the club had been resigned to losing Barkley for some time.
And now, barring late hitches, he is likely to secure a move to Chelsea.
It will mean the player is leaving Goodison Park after 13 years, having joined Everton as an 11-year-old in 2005.
The academy graduate has played 150 times for Everton in the Premier League, scoring 21 times since making his debut in 2011.