Guus Hiddink has set Chelsea the target of over-taking Manchester United by the end of the Premier League campaign.
Winning the Champions League and the FA Cup are the top priorities for last season's champions, who moved up to eighth place in the table thanks to a 2-1 win at Norwich City on Tuesday.
A top four finish has long been established as the norm at Stamford Bridge in the Roman Abramovich era, but Hiddink knows that it remains a tough task to achieve that aim this term.
United, in fifth, seem more catchable and are currently five points ahead, although that could change when they play Watford on Wednesday.
Fifth spot will qualify the team that finishes there for the Europa League, as will winning the FA Cup.
"Are they catchable?" said Hiddink when asked about United. "Well, first of all, we're happy. It's not Chelsea standard to be happy to be out of the relegation zone, and sit back and relax a bit.
"We have to set new targets now with the ambition of Chelsea in the direction of Europe.
"We have a tight schedule — Stoke, PSG, Everton — and the squad is not very, very broad, so we hope everyone is on board.
"If everyone is available, we'd like to go as high as possible towards the European spots."
Chelsea took the lead at Norwich after just 39 seconds when Kenedy scored and Diego Costa doubled the lead in first-half stoppage time, albeit from an offside position.
That gave them enough of a cushion to repel a spirited fightback from Norwich, who saw Nathan Redmond pull one back.
Hiddink made it clear he was happy with the result but the performance could have been better.
"We have now won a few games in a row, which gives satisfaction of course," he said.
"But I think we were a bit sloppy in the finishing in the first half.
"We had a splendid start through Kenedy, a beautiful goal, but after that we had some options to get a second.
"We did in the end, but we should have killed it off already by then. I'm satisfied with the result, but I like to be critical that we didn't finish it off early."
It wasn't the first time this season that Chelsea have benefited from an offside goal and Hiddink sympathised with the Canaries, who dropped into the bottom three.
"I haven't seen it yet but, if so, I can understand people are frustrated in the other dressing room," he said.
"If that's the case, I can understand their feelings."
Norwich manager Alex Neil was confident that the players would not be affected by the current league table.
"I don't think psychologically it will have a part," he said. "We have Swansea on Saturday, Man City and then games against teams around about us. We're capable of winning those games.
"We need to win games to stay in this league. The fact we're in the bottom three now has no bearing. We've been there or about all season. We have to win games to get us out of there.
"We're playing teams around us. Teams like Bournemouth might be playing teams at the top. Everybody has everyone to play."
Neil was frustrated that the relevant linesman did not spot that Costa was offside for the second goal.
"I made them aware that he'd got it wrong at half-time," he said. "The guy's made an honest call and got it wrong. It happens.
"I won't lambast him for that. Of course we're disappointed and frustrated, but there we are."
Norwich midfielder Alex Tettey was taken to hospital for an X-ray on a leg injury, while Robbie Brady and Gary O'Neil were hurt when they collided in the second half.