The Championship side have already made six signings this summer, but Monk has hinted that that number could soon rise.
Leeds manager Garry Monk
The Whites have already brought six new players to Elland Road this summer, including three permanent signings and three loan deals, but there are still some areas for concern in Monk's squad ahead of the new season.
Kemar Roofe is one of six signings Leeds have made this summer
However, the newly-appointed United boss has suggested that those concerns may well be addressed imminently.
"We're working very hard to get the right players and we're very close to a few of them. If they can happen in the next few days great. If not, we'll stay patient," he told the Yorkshire Evening Post.
"I'm only going to bring in players who will better us. Of course we'd like to bring in the players we want straight away but it's not always from one end. There's two ends to making a deal."
Given the current state of the squad, most supporters will surely be hoping that a new centre-back is the next addition that Monk makes.
Liam Cooper has missed much of pre-season through injury, leaving the likes of Toumani Diagouraga and Luke Murphy to fill in at times. And with Kyle Bartley and Sol Bamba being the only other senior options, Monk will surely know that their task of enjoying a good season will be much tougher if they go into the campaign with just three centre-backs.
He may also want to consider adding more depth at full-back - especially given that speculation linking Charlie Taylor with a move away refuses to die down (via Yorkshire Evening Post) - while central midfield could also perhaps do with strengthening following Lewis Cook's departure and the end of Liam Bridcutt's loan.
Liam Bridcutt enjoyed a promising loan spell at Elland Road last season