But he is reluctant to say just how many more new signings will arrive at Anfield before the transfer window closes at the end of the month.
"I don't know whether I expect more signings to follow rapidly after Joe arrives, but certainly our hunt continues," he said. "I said when I first came in my objective was to build a squad that was going to be competitive.
"Hopefully between now and the end of August we can get some more players in who can help the players we have here. That would be great.
"I don't really want to say how many I'd like to bring in because if I say three, for instance, then people might say "you've not got three" if it doesn't happen.
"We still have work to do in the market and we hope to get it done sooner rather than later, because we want to give them as much time as possible to settle in.
"But I'm realistic enough to know that these things can take time. The people behind the scenes are working very hard on the targets I've asked to come in."