Chelsea boss Jose Mourinho values Belgium playmaker Eden Hazard at £200m after reported interest from Real Madrid.
Alan Pardew is weighing up chasing a big-name summer signing to boost Crystal Palace's profile.
Goalkeeper Fabianski has joined the Swans on a four-year deal following the end of his contract at Arsenal, and Monk believes his arrival is a statement of intent.
Swansea are now looking to make a number of other signings to push them forward for next season, although Monk accepts that they will probably miss out on some targets.
"I am excited about what we might be able to do this summer of course," Monk said in the South Wales Evening Post. "I know how I want to do it. I know what players I want and I know what to say to people.
"We are not going to get every deal done, but that's part of the process - that's the way it works.
"But I think we have proved already that we can attract good players to the club by signing Lukasz Fabianski, and I am hopeful that we can get a few more."
Monk added: "I have been in every single day since last season finished.
"I am looking at player recruitment — talking to agents, studying players, trying to find the right ones for us."
Monk believes the chance to play for Swansea would appeal to many players, while he has no worries about his own ability to lure top-quality performers.
"The attraction for them is the Premier League and the way Swansea City are as a club," he said.
"We may not have a massive name, but football does the talking at the end of the day.
"I know the game inside out and it's up to me to show that I can get players to come here."