Mosley is aiming for his third straight victory since losing to Anthony Mundine at the Allphones Arena in Sydney, New South Wales, Australia in 2013.
But before he gets serious about his call, Mosley wants to secure the WBA interim welterweight belt against Avanesyan on May 28.
“He is a good fighter. He punches hard. He works hard and he has something I want. He has that belt,” Mosley said.
The 27-year-old Avanesyan lost only once in his pro career. He is an orthodox fighter and has a 48 percent knockout rating.
In 2010, Mosley nearly knocked out Floyd Mayweather, Jr. in the second round of their title fight but he failed to make a follow up as Mayweather held and survived the round to win via unanimous decision.
Three years before facing Mayweather in a title fight, Mosley has already lost to Cotto but he had shown impressive wins over Ricardo Mayorga and Antonio Margarito to earn a shot at Mayweather.
In 2011, he challenged Pacquiao but lost via a unanimous decision. Later in 2012, he also lost to Canelo Alvasrez via a unanimous decision.
“Like I said before, I want a Pacquiao rematch. A rematch with Mayweather and a rematch with Cotto. I also want a fight with Juan Manuel Marquez. After my fight on May 28th we can get it on,” said Mosley.
Mosley is on a winning mode having won over Ricardo Mayorga in a rematch via a unanimous decision. He also made an impressive performance over Patrick Lopez in Panama which he won via TKO. Both fights happened in 2015.