The 25-year-old said that he is ready to face the best in his division, which means unification bouts.
Price per head services saw that in Spain, the WBA super-bantamweight world champion was at ringside to see Martinez stop Jeffrey Mathebula in nine rounds and keep the IBF belt.
And even though Frampton apparently turned his attention to WBC champion Leo Santa Cruz, Quigg has no doubts about facing Martinez.
“Definitely,” he told Ringside. “That’s what I’m hoping for in the summer. A fight between me and Martinez is on my radar.
“That was the best I’ve seem him box (in Spain). He mixed up his shots well, me and (trainer) Joe Gallagher were ringside saying this is the best he’s boxed.
“I think Mathebula got his tactics wrong; he was moving way too much, giving Kiko momentum and once he gets it, it’s hard to get to him.”
Quigg suggested that this summer, number one Guillermo Rigondeaux and number two Santa Cruz are also on his shopping list.
And pay per head sportsbooks saw that Frampton again came into the equation, but he insists that in March his promoter Eddie Hearn offered him the fight, only it to be turned down by ‘The Jackal’.
Last week the same was said on Ringside by the Northern Irishman, and he called Quigg, “robotic”, “programmed as a fighter” and said that his main weakness is his chin.
However, the world champion warned that he is better than Frampton believes, and many pay per head sportsbooks agree.
“To be honest I think I am a pretty good programmed fighter!,” said Quigg. “He goes on about my main weakness being my chin.
“I’ve never been put down in sparring – unlike someone, who’s been put down with head shots and body shots. I am talking about him!”
Pay per head sportsbooks saw that early in his career, Quigg was put down twice, but he was still able to win the fights, and says that it puts him up next to another of the four current British world champions.
“Early on in my career I was basically learning on the job and I have put those mistakes right,” he said.
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“Look at Carl Froch. He was put down, so he gets back up and he goes on to win. Same here.”