Fury called Joshua a "chicken" and a rematch between him and Wilder looks inevitable in the wake of their controversial draw.
Joshua holds the WBA, WBO and IBF titles, the belts that Fury won when he beat Klitschko in 2015.
In the ninth, Wilder threw 46 punches, with 13 of them landing, while Fury only landed seven of 24. I don't know what fight he was watching.
In his role as Fury's promoter, and alongside the British Boxing Board of Control, he has made a complaint to the WBC over the scores that meant their thrilling world heavyweight title fight, at Los Angeles' Staples Centre, concluded as a draw.
Negotiations for a fight between Wilder and Joshua broke down earlier this year, but Finkel is willing to go ahead provided that talks with Matchroom Boxing boss Eddie Hearn remain private.
"They wanted to get you because they assumed you was finished!"
With his fighter's reputation enhanced, Warren told Press Association Sport: "You'd think they'd want the rematch". It was one of the most exciting fights - certainly the most exciting I've seen at heavyweight in America since Lennox Lewis-Vitali Klitschko (in 2003).More news: XFL announces its eight home venues, including four National Football League home fields
Fury came back from two knockdowns, including a heavy fall in the 12th round, to reach the final bell against Wilder.
"If it's something that people would like to see again we would absolutely love to do it".
Wilder retained his WBC heavyweight title after the judges returned a split decision that earned much ire from pundits and fans, with most considering Fury the victor despite having to twice climb off the canvas.
"I'm quite sure Mr Sulaiman [Mauricio Sulaiman, WBC president] - being the proud Mexican that he is - will want to make sure there is a rematch as his judge got it wrong".
Following the fight he said: "It's an iconic comeback, isn't it?" "How on Earth he gave the first four rounds to Wilder, I don't know".
Joshua last fought in September, when he successfully defended his belts by stopping Alexander Povetkin in seven rounds at Wembley.