Hamed, due to defend his World Boxing Organisation featherweight title against a yet-to-be-named contender in November, said he has offered to fight Espinosa on five separate occasions, "but he keeps refusing".
Espinosa, a former long-time World Boxing Council featherweight champion, lost his title to the Mexican Cesar Soto on 15 May in an unanimous 12- round decision.
Asked why Espinosa was backing off from facing him, Hamed said the Filipino was probably afraid. "I don't blame him. I don't want to fight with me," said the 25-year-old champion.
Hamed, who has an impressive record of 32 wins, no defeats, with 29 knockouts, expects to have his next fight at Caesars Palace in Las Vegas on 6 November.
"We don't have the contender's name but he's likely to be Mexican," said Riath Hamed, the champion's brother and manager.