The west London side were handed a lifeline on Tuesday night after Brighton and Hove Albion held fourth-placed Tottenham Hotspur to a 1-1 draw at the Amex Stadium.
Spurs are sat in the final Champions League qualification spot and eight points clear of the 2017 Premier League champions.
However, Chelsea FC have played one game less than their north London rivals and can reduce Tottenham’s advantage to five points with a win at Burnley.
The Blues are looking to record successive Premier League victories for the first time since 30 December following a difficult run of Chelsea FC.
Speaking at his pre-match media conference ahead of Chelsea FC’s trip to Burnley in their next Premier League game, Conte said:
“I think we have to try until the end to reach this target [finish in the top four].
“If you want to be realistic, with five games to go it is not simple to reduce the gap. We must have the will to fight, we must have the desire to try to take this target. Why not?”
Chelsea FC haven’t won the Champions League title since 2012 when the Blues beat Bayern Munich on penalties.
The Blues lost 4-1 on aggregate to La Liga giants FC Barcelona in the Champions League round of 16.
Conte has faced intense speculation surrounding his future at the west London side following their disappointing defence of their top-flight crown.
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