Wilder is due to face Robert Helenius in October, 12 months after suffering a second straight stoppage defeat by Tyson Fury.
If Wilder can get past Finland’s Helenius, the 36-year-old could be in line for a clash with another Briton in the form of Joshua, who was last month outpointed by Oleksandr Usyk for the second time in 11 months.
“It really depends mentally what Joshua feels he needs,” Finkel told The Sun.
“If he needs to take a break and take a fight as a comeback fight, or if he feels the real redemption is with Deontay, we’re open to it.
“He was gutsy to go right back into the [Usyk rematch] when he clearly lost the first one.”
Joshua, 32, lost the WBA, WBO, IBF and IBO heavyweight belts to unbeaten Ukrainian Usyk in their first fight, last September, before failing to regain them in last month’s rematch.
Meanwhile, Wilder retained the WBC title against Fury with a controversial draw in 2018, before losing the gold to the unbeaten Briton in 2020. Wilder was unable to win back the belts in a trilogy bout with Fury last October, as he lost via TKO – as he had in the pair’s second in-ring meeting.
Following Joshua’s most recent loss to Usyk, “AJ” seized a microphone and delivered a strange monologue, in which he talked up his own career.