Dalglish has added Charlie Adam and Jordan Henderson to his midfield and remains favourite to land Aston Villa's Stewart Downing after having a ?15million bid knocked back last week.
A number of fringe players could be set to leave Anfield and Dalglish said: 'We are happy with the business we have done so far.
Reds on tour: Charlie Adam (left), Jamie Carragher and Kenny Dalglish (right) in Guangzhou
'Hopefully we will do some more business before the window closes but I'm not going to give names because that's disrespectful.
'We are looking to bring other players in and that could mean we expect some to leave. That's football but we have a while to go yet and we'll see what we can do.'
The one they want: Stewart Downing
Adam flew out to China for a mini-tour of the Far Eastbut Henderson has stayed at home after playing for England Under 21s at the European Championships in Denmark.
Skipper Steven Gerrard and goalkeeper Pepe Reina have also been left behind but the key pair should be fine for the start of the campaign.
Gerrard is continuing his rehabilitation from groin surgery which ended his campaign in mid-March while Reina had a double hernia operation last month.
'Steven is injured at the moment and that's why he's not here with us,' said Dalglish in Guangzhou, where the team will play their first friendly in China on Wednesday.
'He has made a fantastic recovery from his operation towards the end of last season.
'He just needs to get the final couple of niggles out of the way and then he will be fit for the start of the season against Sunderland.
'I know people are disappointed he isn't here with us but the disappointment would be far greater if he couldn't play the first (Premier League) game.
'That is why he has stayed at home, to rest and to have the best chance of being fit for the start of the season.
'The same situation applies to Pepe (Reina) - he had a double hernia operation in June.
'He isn't fit and so had to stay at home. He should be ready for the start of the season.'
On the mend: Liverpool captain Steven Gerrard has not played since March
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Source: Daily Mail
Source: Daily Mail