Chelsea signed Havertz from Bayer Leverkusen in September in a deal worth more than £70million.
The 21-year-old has made 13 appearances under Frank Lampard this season, scoring four goals, three of which came against Barnsley in the EFL Cup.
Asked about Chelsea’s start to the season, Leboeuf told ESPN: ‘I think it’s getting better, some players are getting better.
‘I’m very pleased for Hakim Ziyech, getting fit and giving his best. But I’m still not convinced about Kai Havertz, I still want more from him.
‘I want more impact from him where I think he disappears. I’m sure Frank is still not completely happy with the way they worked together.
‘Sometimes it seemed like they were looking for each other like they don’t really know each other.
‘I’m looking for something better, much better from Chelsea. With the players they have, they’re capable of giving much more than we saw.
‘Even though they got the win, the clean sheet, everything was going their way, but I can’t be happy with the performance 100 per cent.’
Havertz started for Chelsea on Saturday as they beat Burnley 3-0 to climb to sixth in the Premier League table.
Ziyech scored his first Premier League goal in the fixture and said afterwards: ‘It’s been a good week for me.
‘Hopefully we can continue. I feel good and feel at home. Everything is fine.
‘Burnley had one chance at the beginning, but after that we controlled the game. You need to play with confidence and not be afraid to make mistakes.
‘Otherwise it won’t go how it’s supposed to go. Every week we make steps. Let’s keep it that way.’