"First of all, I want to congratulate Anthony Joshua on his win last Saturday night".
After 12 rounds, Britain's Joshua triumphed 118-110, 118-110, 119-109 on the three judges' scorecards.
IBF and WBA world heavyweight title holder Joshua won the unification bout against WBO champ Parker on a unanimous decision.
"That fight, in terms of ability, is getting closer and closer because Joshua is learning and improving all the time".
Wilder, yet, the unified-heavyweight champion has insisted he's not leaving the U.K, effectively ruling out a fight across the pond. A unification fight with Wilder is the biggest fight on the table and in the sport at the moment.
Boxing fans around the world will hope Joshua secures a huge unification fight against Wilder next.
This fight is no longer a matter of if it will happen, but now when it will happen and where.
Joshua and his opponent from New Zealand went into this fight unbeaten, but the British overcame Parker who has never been down according to the commentator of the fight.
"I know the bookies say I might get a knockout but forget the hype, Parker was a world champion", Joshua said.
Costello didn't leave it there though, claiming that Fury could be running out of time if he wants to beat the 28-year-old. He has trash talked both fighters on their disappointing performances. And if Joshua can't get in on Wilder and is forced to fight him on the outside from a distance, as he did against Parker, it's not hard to envision him losing.
Anthony Joshua swings with his left against Joseph Parker in Cardiff. Also, styles make fights and although Wilder can't do all that Parker can, he has weapons like power, reach and awkwardness that could be a stumbling block for Joshua.
Perhaps the biggest threat lies outside the heavyweight division in Oleksandr Usyk (14-0, 11 KOs), the Ukrainian who holds two cruiserweight world titles and faces Murat Gassiev for the other two on May 11.
Miller is ranked third in three of the four sanctioning bodies; WBA, WBO and IBF.
The London 2012 Olympic champion was in more considered mood at the post-fight press conference.
"The only way to do that would be in the ring against Anthony Joshua, and he should keep those comments to himself". He will come again an will ultimately challenge once again for a world title, he has proven that he belongs at the top with Joshua.
However, the American's co-manager Shelly Finkel has quashed any doubts of the possibility of the fight, insisting that the 40-0 fighter is willing to fight in the United Kingdom this summer.