Brendan Rodgers has claimed Liverpool would not settle for fourth place at this stage of the season because of a growing belief they can challenge for the title.

Liverpool won at Stoke City on Sunday for the first time in the Premier League and the 5-3 result, coupled with Daniel Sturridge's return from an ankle injury, has increased Rodgers' confidence that his team can maintain a challenge alongside Arsenal, Manchester City and Chelsea. Rodgers also said he believes Sturridge can emulate Luis Suárez's world-class form.

Liverpool are six points behind Arsène Wenger's leaders but Arsenal, City and Chelsea – along with Everton and Tottenham Hotspur – have all to visit Anfield before the season is over.

Rodgers' target at the start of the campaign, shared by the principal owner, John W Henry, and the chairman, Tom Werner, who will attend Saturday's home game against Aston Villa, was to return Liverpool to the Champions League after a four-year absence. But he insists his fourth-placed team are aiming higher.

"Manchester City, Arsenal and Chelsea are based around Champions League squads," the Liverpool manager said. "They have been in there religiously and they have got a lot of depth that they can call upon. But if we have the fortune to stay clear of injury and whatnot, I would put our team up against anyone. I would never give up the fight.

"Of course, the challenge is to get to fourth. Once you can do that, it is all about seeing if you can go beyond that. But I will never give up the fight [for the title] with the games we have got to go and the confidence we have in the team. In terms of the message the manager transmits to the squad, I've always tried to be optimistic. We work hard on that and the consequences are the results on the field and gaining confidence.

"It's a long way to go, but you can see it's an open Premier League so the team that can make the least amount of mistakes and continue to evolve can hopefully win out at the end. We know where we are heading and the direction we are going and at the moment we are going in the right way."

Sturridge returned from a seven-week absence with a goal and an impressive assist for Suárez against Stoke. His manager believes the England international can only get better.

Rodgers said: "Daniel has a wonderful opportunity over the next few years to become world class. He has every tool and every quality he needs to be as [good] as Luis Suárez. If he stays clear of injury and stays on the field he can achieve that. It signified how hard he'd worked while he was out that he could come straight into the game at Stoke and make such a big impact."

The Liverpool manager reiterated his belief that January will be a quiet transfer window at Anfield and all the leading clubs in the Premier League, although he will discuss targets with Henry and Werner this weekend. "The owners have been great in terms of, if there is something to be done that will help us, they will support that," said Rodgers.

"I just think it will be a difficult market to improve on but it certainly won't be for a lack of trying. We are assessing a whole raft of players, it is just a question of whether they are going to be available to bring in now."