Moyes was interested in signing Sporting Lisbon's Joao Moutinho and Manchester United's Darren Fletcher, but in neither case were they successful.
"It's now getting to the stage where you are wondering how long it takes for new players to settle," added Moyes.
"I'm hoping we will have some in (before the start of the season).
"But I'm not going to turn around and say I am totally confident because you never know what happens."
Striker Andy Johnson looks likely to join Fulham but Kenwright insisted the club did not need to sell anyone to bring in new players.
"Our attempts to complete the signings of players we believe will improve the quality of our first-team squad continues on an hourly basis," he said.
"We have had a budget for incoming transfers since the start of the summer - and that budget is in no way reliant or dependent upon either the proposed relocation of the club to Kirkby or the sale of current players."
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