The Bluebirds play Sky Bet League Two side Accrington Stanley in the Capital One Cup second round on Wednesday and are expected to rest several players following their 3-2 Barclays Premier League win over Manchester City.
Summer signing Andreas Cornelius could start the cup match and, while the next fixture is on his mind, Mackay said he was still working hard to recruit another player.
"We're trying hard and we're going to make sure we do everything we can right up to Monday," Mackay told BBC Sport.
"We would like to at least get one more in, but it's not easy because they have to be players that bring more quality, rather than the quantity of bringing three or four people in in the last week and just filling up a squad.
"I've got good players here, I've got very good players here, whoever comes in has to add to that.
"That being the case, we are still trying. We are under competition from other (clubs) because that's what good players bring.
"But we're trying hard and we're going to make sure we do everything we can right up to Monday."
Mackay believes the win against Manchester City so early in the season will give his side the confidence they need to do well.
"The atmosphere in the city was incredible," Mackay said.
"The result and the way the players showed they are capable of consistency, that's what every manger and every player strives for.
"It shows them that belief they can play at that level against some of the top players in the world."