The veteran goalkeeper is well versed in the art of trophy-collecting, having lifted a number over the course of a distinguished career.
He is looking for another winners’ medal to be delivered in 2018-19, in what could be his final campaign with the Gunners as his contract runs down.
Cech, 36, said of Arsenal’s targets: "Our priority is to get into the top four [so we can] be in the Champions League and then you want to progress and evolve as a club, as a team.
"We have a new manager and obviously we set our targets so if we can win a trophy together in the first season it would be a good achievement.
"You play every game to win and this time we were in the FA Cup, we have the tradition as a club to do well and if we can win it, we'd like to do so.
"It is the same with the Europa League – we started really well and are in the last 32.
"These are two targets but the Premier League remains a big objective, to get into the top four."
Arsenal kept themselves in the hunt for another FA Cup during their last outing, with a 3-0 third round victory enjoyed over Blackpool.
Unai Emery’s side made light work of League One opponents on the day, but it was an eventful trip to Bloomfield Road for the Gunners as they found themselves caught up in the ongoing protests of the home support against owner Owen Oyston.
"We started with the guy sitting on our bus,” said Cech.
"We had to change the bus. It was one of those things that were aware of and we knew that something might happen.
"We tried to concentrate on our game, on our performance and obviously after that you think 'okay, something might happen during the game' but we were ready for it.
"We knew that we have to concentrate on our performance. We did it really well."