Coppell has added midfielder Kalifa Cisse to his squad but is weighing up whether he needs more players.
"I would like to have got someone else in by now," said Coppell in the Reading Evening Post.
"I make no pretence about that, but I am reasonably comfortable at the moment with what we've got.
"We fly off to South Korea for three games and then after that I will have a lot clearer indication of where we're at, so after that I will make a judgement call.
"We will probably pick up players towards the start of the season.
"The automatic assumption is we definitely will, but we only will if it's the right business and the right sort of player.
"I make no apology for that. We won't buy for the sake of buying."
Coppell's side play River Plate, Lyon and Shimizu in the pre-season tournament and could have another match if they qualify for the final.
The club want to agree fresh terms with striker Leroy Lita, who has not travelled on the tour as he is recovering from the European Championships with England Under-21s.
Nicky Shorey is also negotiating a new contract, while Stephen Hunt put pen to paper earlier in the week.
PA Sport