If Chelsea beat Stoke at home on New Year's Eve, they can equal Arsenal's record 14-game winning sequence from 2002 when they play Tottenham at White Hart Lane on 4 January.
"If you ask me, I hope to continue until the end of this season", said Conte, with a smile.
"It didn't happen, I am pleased for this, because I can count on all my players in the squad".
Antonio Conte's league leaders - who put the pressure back on the chasing pack - shrugged off the absence of suspended talisman Diego Costa, with replacement Pedro's stunning first-half goal setting them on their way.
"It's a fantastic run, but it's important to continue that now".
Klopp also believes he is more prepared for the Premier League's frantic festive fixture schedule this time round.
Yes because we win every game!
The win meant the Blues have now won 12 Premier League matches in a row, while also firming their grip at the top of the table.
"I don't think it is a case of which Bournemouth side turns up, I think we have been inconsistent - our performances have shown that".
I don't know if it's the best Chelsea I've played in but it's a good team.
Willian was pushed further forward to help Chelsea compensate for being without top scorer Diego Costa
English Premier League scores and goalscorers on Boxing Day, with Chelsea, Manchester United, Arsenal and Manchester City all picking valuable three points to remain in the hunt to the title this season.
"To win 12 games in a row is not easy in this league", he told BBC Sport.
"I think that was probably where we fell short".
However, the Blues manager opted to start with Hazard in an advanced role supported by Pedro Rodriguez and Willian for the visit of the Cherries.
- Fabregas has scored or assisted in each of his last three Premier League starts for Chelsea (one goal, two assists).
Conte opted to employ Hazard as a central striker, forcing 23-year-old Belgian worldwide forward Michy Batshuayi to continue his wait for a first league start since his £33 million ($40.5 million, P2,015,535,396) arrival from Marseille.
"They look like champions at the minute, for me at the moment they're the best team in the league", said Wilshere, as quoted by the Goal.
Burnley edged away from the danger zone with a 1-0 win over fellow-strugglers Middlesbrough and Sam Allardyce's first match as Crystal Palace manager ended in a 1-1 draw at Watford. They're not on the same level yet, but when we consider the success of Barcelona and Real Madrid in recent years, it's by having a deadly trio of attackers that has made them appear unstoppable at times.
With the game over as a contest, Fabio Borini grabbed a superb consolation as he chested down 25 yards out before volleying home to the top-left corner.