The Blues have stormed into an eight-point lead at the top of the table with just 13 games remaining and are favourites to progress into the quarter-finals of the FA Cup ahead of Saturday's clash with Championship side Wolverhampton Wanderers.
Conte is expecting a difficult test at Molineux, but urged his side to continue their winning mentality in order to pick up the two trophies still available to them.
"Usually I like to win and I like to try to win with my team, every competition in every season. We must have this winning mentality. When you are Chelsea's coach or you are a Chelsea player, you must have this ambition to try to win every competition that you play," he told reporters.
"For sure it won't be easy. In the league there are six teams very strong to fight until the end to win the title. In the FA Cup there are 16 teams. Our target now is to go into the next round. Tomorrow the game won't be easy. Don't forget Wolverhampton won against Liverpool away, won against Stoke away.
"We must pay great attention, because this team showed in the recent past that they have the possibility to beat great teams. I hope tomorrow the result will be different and Chelsea to go in the next round."
Chelsea last won the league and cup double under Carlo Ancelotti in 2010.