Daniel Agger's future at Liverpool has been cast into fresh doubt after his agent indicated the Danish defender would be open to a move to Barcelona.

Liverpool rejected a €17m (£14.6m) offer for Agger from the Spanish champions last week amid concern over their central defensive options. Brendan Rodgers responded by appointing the 28-year-old as the new vice-captain following the retirement of Jamie Carragher.

With Carragher gone, Sebastián Coates failing to convince Rodgers and Martin Skrtel's position uncertain having been told he can leave Liverpool earlier in the summer, only to be informed last week that he would not be sold, the Anfield club can ill afford to lose their most influential centre-half. That was reflected in the response to Barcelona, who have targeted either Agger or David Luiz but have received no encouragement from Chelsea that the Brazil international is for sale.

Barcelona are expected to return with an improved offer for the Liverpool defender before the transfer deadline. And Agger's agent, Per Steffensen, has suggested the Denmark international would consider a transfer to Camp Nou.

"We are aware that Barcelona have made an offer for Daniel that Liverpool have rejected," said Steffensen, who was approached by an agent representing the Spanish club several weeks ago. "Daniel has a contract with Liverpool for the next three years and it would be up to the clubs to agree a fee for his transfer in order for that to change."

Agger's departure would be a serious setback to Rodgers, who has struggled to add quality additions to Liverpool's defence this summer, signing only Kolo Touré on a free transfer from Manchester City so far. Liverpool are, however, believed to be close to the £5m signing of Granada's left-back Guilherme Siqueira.

Rodgers' pre-season preparations have already been disrupted by the Luis Suárez transfer saga and the arrest on Thursday of Raheem Sterling for common assault. The England international is due to stand trial in September and sat out Saturday's friendly 1-0 defeat by Celtic as a result. "I just thought he had been through a lot," the Liverpool manager said. "He hadn't slept at all in the last 48 hours and adding to that Jordan Ibe has been excellent and at 17 he is showing great promise. That was all it was, to protect Raheem."

One positive from the Dublin friendly was the second-half performance of Daniel Sturridge, who returned ahead of schedule from an ankle-ligament injury to enliven an otherwise laboured Liverpool performance. With Suárez banned for the first six matches of the season, irrespective of his long-term position at the club, Sturridge will have greater responsibility when the campaign opens and Liverpool have arranged a behind-closed-doors game on Monday specifically to improve the striker's match fitness.

"I think he is aware of the opportunity in front of him," said Rodgers. "There were maybe teething problems when he arrived in January but once he got his head around that and the demands of playing at a big club regularly, then he was terrific. He was in really good form at the end of last season, which got him called up for England, and it was unfortunate that he got a bad injury. But I can have no complaints at how he has worked. He is actually ahead of schedule coming back and I am sure that this season he can demonstrate that he is a top striker."

Rodgers is adamant Liverpool will add quality additions to their squad before the transfer window closes, having been frustrated on several major deals this summer including the £21.8m offer for Diego Costa. The Brazilian forward is now expected to sign a contract extension with Atlético Madrid.

"There is an awful lot of work going on behind the scenes and it is not easy as we have seen from other clubs' experiences as well," the manager added. "But I am confident that we will add to the team. I don't think there is any doubt we need that. The players we have brought in have added great depth and support to the team, but that bit of quality now coming into the group could really set us up. Everyone at the club, the recruitment team, the board and myself, are working hard to make that happen."