Conte backs Hazard to take the central role in Chelsea charge.
Forced to settle for a 1-1 draw at Liverpool on Saturday, Chelsea is lagging 11 points behind runaway leaders City.
If Conte's side is to have any chance of catching the Premier League pace-setters, they must reel off the kind of lengthy winning streak that catapulted them to the title last season.
Key to Chelsea's hopes of emulating that burst in the form of Belgium playmaker Hazard, who looks back to his best after an injury-hit start to the campaign.
Hazard was outstanding playing alongside Alvaro Morata at Anfield and Liverpool found it impossible to subdue him.
The 26-year-old often dropped into midfield to control possession and Conte feels his flexibility brings a new dimension to the team.
"The start of this season was full of trouble with Eden because he had an injury with the national team and we started the season without him," Conte said.
"Now I think Eden is in really good form and I think he likes to play as a striker.Â
"There is a good link with Alvaro and for me also it's a great opportunity to play with two different systems."
Although Chelsea is unbeaten in their last five league games, it has been a turbulent season for Blues boss Conte.
Frustrated by Chelsea's failure to land his top transfer targets in the close-season, Conte has cut a tetchy figure as the pressure of defending the title and challenging for the Champions League starts to mount.
The Italian's mood hasn't been helped by City boss Pep Guardiola masterminding a major transfer overhaul and watching his spending pay rich dividends.
- Conte worried -
City looks unstoppable at present after taking their winning run in the league to 11 matches with a victory at Huddersfield Town at the weekend.
"I think Manchester City in this season is a strong team. Also last season, Manchester City was a fantastic team. Then, after the transfer market, they bought their first targets and then they have improved a lot.
"They can do this also in January maybe, in the future. For this reason, we must be worried," Conte said.
While Conte frets about Chelsea's prospects, the club's goalkeeper Thibaut Courtois takes a more optimistic view.
"December is a very tough month. Maybe they drop some points," he said.
"We have to be there to keep on winning and hopefully close down on them, then towards the end of the season maybe overtake them."
Swansea could be easy pickings for Chelsea as Paul Clement's side arrive at Stamford Bridge second bottom of the table after a five-match winless run.
A dour goalless draw with Bournemouth on Saturday did little to improve Clement's job security after the former Chelsea assistant was reported to be on the verge of the sack last week.
Clement admits confidence has been low at Swansea of late, but he insists his players still believe they can put together a winning run and climb out of the relegation zone.
"It's no secret the team has been down in confidence, but the running and battling was strong and we played some good football," Clement said.
"I would have expected us to be in a healthier position than what we're in.
"You know anytime you put together back-to-back wins, or a win and a draw, you're pushing out of those danger zones.
"Our form has not been particularly good, but that's the belief we have."
