Mohamed Salah says the club is aiming to win every trophy on offer.
The Blues came pretty close to both prizes last season as they finished four points behind Manchester City in the title race, and reached the semi-finals of the Champions League, but were knocked out by Atletico Madrid.
At the start of his second spell in charge at Stamford Bridge last season, manager Jose Mourinho said his first season back at the helm was about the evolution of a side, and didn't expect any silverware within his first 12 months back at the club.
This season may be different, as Salah told the Chelsea website: "The aim is for us to win the Premier League and Champions League. It’s important for a club like Chelsea to challenge for every competition we enter and hopefully we can do that.
"In terms of myself, I don’t usually like to set too many targets but I just want to improve as a player as much as I can and help my team-mates become successful."
The signings of Cesc Fabregas and Diego Costa in particular are likely to provide extra quality to the Chelsea side that is enough to bridge the gap between themselves and the top of the table.
Bookmakers certainly make Chelsea amongst the favourites for the big prizes next season with the Blues favourites to win the league title at 19/10 - though their chances of being successful on the continent seem more difficult as they are priced up at 11/1.
Given the manager's pedigree, along with the talent in the squad, you'd be a brave person to bet against Chelsea being in the mix for both prizes at the business end of the season.