Jordan Henderson believes Liverpool will challenge for major honours next season despite Jürgen Klopp’s frustrations in attempting to land two prime targets, Naby Keita and Virgil van Dijk.

Liverpool have added their record signing, Mohamed Salah, and Dominic Solanke to their ranks this summer and hope to conclude a deal for Hull City’s left-back Andy Robertson. The club has also refused to concede defeat in the pursuit of Keita despite RB Leipzig’s repeated insistence that the midfielder is not for sale. Attempts to add Van Dijk to Klopp’s defence have also been resisted by Southampton but the Dutch international’s future remains uncertain.

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Henderson insists Liverpool will improve on last season’s fourth-place finish in the Premier League regardless of what materialises in the remainder of the transfer window. The long-serving midfielder Lucas Leiva has flown to Italy to finalise a £5m move to Lazio having said his goodbyes at Melwood on Friday.

The club captain said: “We have to set it very high with the squad, the players we have got and the manager we have got. We want to be winning things. That is the aim. We will go into every game and every tournament we are in wanting to win. We have to set the bar very high. There is plenty of competition for places. We have a fantastic group of players who want a better season this year and we will be working as hard as we can to impress the manager to get into the team.”

Henderson suggested Liverpool’s squad needs only fine-tuning after several summers of extensive recruitment. He added: “We always want to improve as a team. We have brought a couple of players in and have a couple of players coming back from injury. Everyone wants to improve and I think we have a young squad, getting better and learning. Last year put us in good stead moving forward and hopefully we will have a better season.”

The England international made his first appearance in five months for Liverpool at Tranmere Rovers on Wednesday having recovered from the latest foot injury to interrupt his Anfield career. Henderson, who also featured in the 1-1 draw at Wigan Athletic on Friday, trained at Melwood throughout the summer to regain full fitness having been sidelined since February by the problem.

He explained: “I got a bad kick in training on the top of my foot. At first I thought it was just a bruise but it kept getting worse and then we had to get a scan and it was quite bad. That is where it all started. I was devastated. I was feeling good – the best I have ever felt – so to have a blow like that late on in the season when it was such an important time for us as a team was a big blow and hard for me to take.

“I just had to keep working as hard as I can. I didn’t manage to get back but worked hard over the summer to get back to this point. I can’t remember when I last had a full pre-season so by the end of it I hope I will be very, very fit.”