Southampton won't accept offers for forward Jay Rodriguez or midfielder Morgan Schneiderlin this summer.
Everton forward Kevin Mirallas has hinted that he will sign a new contract at Goodison Park in the summer.
Liverpool are still looking to bolster their squad before the transfer window shuts at the end of the month, according to manager Brendan Rodgers.
The Northern Irishman has been relatively sedate in his dealings since taking over at Anfield at the start of the summer, adding just Joe Allen and Fabio Borini to his squad.
Two signings are some way away from last summer's big-spending spree under Kenny Dalglish, but Rodgers has not given up hope of adding more new faces before the August 31 deadline.
Speaking to his club's official website, www.liverpoolfc.com, he said: "There has been contact and communication with the clubs. The team of people behind myself are working very, very hard in relation to those targets.
"We hope that within the next number of weeks those will bear fruit.
"The work has been continual right the way through to try and get in players that fit the profile of Liverpool and the team. Like I say, I would hope there would be a couple more signings before the end of August."
While Anfield's arrivals lounge has not been too busy this summer, a number of players, including Craig Bellamy and Dirk Kuyt, have gone through departures.
Consequently, Rodgers has a slimmer squad than the one he inherited and has not ruled out the prospect of more players heading for pastures new.
He added: "We obviously haven't brought in too many players, but there are some players that have gone out for a number of reasons.
"There is still a lot of work to do within the group and there will probably be more changes between now and the end of August in terms of ins and outs.
"Come the end of August when everyone is here, we can be real focused and be together, and start on the journey to hopefully having a real good campaign."