Despite the 12-hour flight time, the humidity and the sometimes draining adulation, Liverpool's tour of Asia was the easy part. Now Kenny Dalglish has the rather more unpleasant task of pruning a bloated midfield.

The Liverpool manager has invested £47m this summer in three midfielders – Stewart Downing, Jordan Henderson and Charlie Adam. However, with the club's owner, John W Henry, tweeting that he expects Alberto Aquilani, who spent last season on loan at Juventus, to stay on Merseyside, Dalglish's room for manoeuvre may be narrowing.

Milan Jovanovic, his most obvious misfit and the last and worst signing made by Rafael Benítez, is close to the exit door. The Serb has had offers from both Anderlecht and Lille, although he said his wife would prefer Brussels to northern France.

Like Maxi Rodríguez and Joe Cole, he was a free transfer on high wages. The three of them, all touted for moves away from Merseyside, are each reportedly on around £100,000 a week.

Rodríguez confirmed last month that he had been approached by his former club, Newell's Old Boys, and said that he was keen to return, despite a fine end to the season in which he scored two hat-tricks.

Cole, the club's marquee signing last year, had been widely expected to leave the club, linked with moves to Tottenham Hotspur, Aston Villa and even Hamburg.

However, Dalglish's assistant, Steve Clarke, who coached Cole at Chelsea when he briefly appeared the most exciting English midfielder of his generation, insists there is still a future for him on Merseyside.

"At the end of last season he was not getting in the team because the team was playing well," Clarke said. "But he has gone away, trained hard and had a good summer.

"Joe Cole is a top international player and he has a big contribution to make to the future. He is the same Joe Cole I coached at Chelsea, just a couple of years older and a little bit wiser. He knows the position he is in. It has been difficult for him because he has not been involved but when he gets the chance it is up to him to take it."

This time last year, Cole was Liverpool's biggest signing despite the lack of a transfer fee. It was supposed to have signalled a change of direction under the newly appointed Roy Hodgson and was a signing endorsed by the club's captain, Steven Gerrard.

In his first Premier League game, Cole was sent off and on his next appearance at Anfield, in the Europa League, he missed a penalty. Dalglish's arrival consigned him even more deeply to the shadows. However, Cole's enthusiasm has seldom faltered, an attribute that may help to keep him at Melwood.

"The better players are always positive," said Clarke. "They see the bigger picture and understand what is going on. They understand they have to reach certain levels and when they do that they will get in the team."