Reports in the British media had suggested Swansea were lining up a move to bring Campbell to the Liberty Stadium when the transfer window re-opens in January.
Campbell, who was part of the Costa Rica side to reach the World Cup quarter-finals in Brazil, has made just two substitute appearances in the Premier League this season.
The 22-year-old striker finds himself behind the likes of Alexis Sanchez, Danny Welbeck and Olivier Giroud in the Arsenal pecking order, but Monk refused to comment on any speculation about a potential loan deal.
"This is the start of who is going where with the window," he said ahead of Swansea's meeting with QPR on Tuesday.
"Of course we are looking at players but in terms of who we are looking at, until something concrete comes up, I will keep names to myself.
"The way I look at each window, I look at the squad, constantly looking at worse case scenario and to have as many options for each position.
"I'm trying to cover all angles if possible. It all depends on who is available, prices, and who wants to come. We need a couple in - hopefully they will be the right ones.
"It's key what type of player they are, what type of person they are. They are worth millions of pounds. There are no guarantees which makes it quite fascinating. All that matters to me is that they come here for the right reasons.
"Even the ones here already it’s about trying to push on. The way this club is, we need young, hungry, dynamic players. That’s what we’re looking for.
"It's either a yes or no on budget. I leave it up to the chairman to negotiate."
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