Usman (16-1) told ESPN on Tuesday that he has been training since February and has offered to defend his 170-pound UFC championship in April, May, June and now July.
Many expected Usman's next title defense to come against Masvidal (35-15), who has expressed interest in a non-title rematch against Nate Diaz in recent days.
If Masvidal is not available, Usman said he'll ask the UFC to book him against McGregor (22-4), a former two-weight champion who has expressed interest in a summer return.
"This is what I have to say: Both [McGregor and Masvidal]," Usman said. "Both guys are champions of Twitter, talking s--- on Twitter. In the history [of MMA], who has ever said no to a title shot? I'm that guy. I'm the boogeyman who these guys are saying no to a title shot against. And they better remain quiet.
"Jorge Masvidal, you had an opportunity on April 18, May 9, June and now July. You want to fight Nate -- a fight that wasn't even competitive. And Conor, you said you wanted to be the king of the 170-pound division. Now you're quiet. So you know what? Just remain quiet. I've given both of you a shot, and none of you have taken it."
Masvidal, 35, hasn't fought since he defeated Diaz via TKO in November in Madison Square Garden. McGregor, 31, had a 40-second knockout of Donald Cerrone in January.
Usman, a former NCAA Division II national champion wrestler, said he would even agree to not take McGregor, who does not have an amateur-wrestling background, to the canvas in the first two rounds of their title fight.
"I will sign a contract with Conor McGregor. We'll put it in the contract: First or second round, I won't take you down," said Usman, who lives and trains out of South Florida and is currently cross-training in Colorado.
"Yeah, if I want you down, there's no ifs, ands or buts about it. But if I want to stand up with you, I will. Am I going to try to knock Conor McGregor out? Absolutely. I'm going to try to knock his head off his F'ing shoulders."