Liverpool chief executive Rick Parry says the club are still looking to bring in new faces before the transfer window closes on 31 August.
Winger Pennant joined Liverpool from Birmingham in July
He told BBC Five Live Sport: "There might be a little bit of business still to be done, we are still looking.
"We might need to get one or two out, it depends exactly on what is available, but we are open-minded."
Parry added the Reds were delighted by skipper Steven Gerrard's comments that he wants to manage the club one day.
"We have made the point we would like Steven to be with us forever," said Parry.
"We know his love for the club is pretty deep so the fact he is saying he wants to be with us long term is the sort of news all our supporters want to hear.
"And the fact the motivation and commitment is there is the main message."
After a couple of years we have at last got the player on the right flank that has been a challenge for us, so we're delighted to have Jermaine Pennant in
Liverpool chief executive Rick Parry
Liverpool's summer signings of striker Craig Bellamy from Blackburn and winger Jermaine Pennant from Birmingham has raised eyebrows because the pair have been in trouble off the pitch during their careers.
But Parry defended the decision and insisted that manager Rafael Benitez has done meticulous homework on the duo.
"Knowing how thorough Rafa is and how conscientious he is, he has been in the Premier League for two years now and has got to know the players better, he would not come to decisions unless he felt confident they were the right players for us," added Parry.
"And we are delighted with the acquisitions we have made this time, they have got tremendous pace.
"After a couple of years we have at last got the player on the right flank that has been a challenge for us, so we're delighted to have Jermaine Pennant in, and we are looking forward to the start of the season."