Staveley and Ghodoussi are exploring a potential takeover of West Ham United, with talks already held with the recently relegated Championship club.
The couple's investment firm, PCP Capital Partners, has been assessing opportunities at several clubs, including Tottenham, before West Ham emerged as the latest possibility on their radar.
Staveley spoke about the kind of project that appeals to her and her husband in an interview with Spear's Magazine this week.
"I think both my husband and I were attracted to building a business where we can take a brand that isn't doing so well, a club that isn't performing well, get it on the right road, and bring that forward," Staveley said.
"There are very few clubs where that can work. If you want to tick every box, there's actually very few clubs that allow that."
Staveley and Ghodoussi led the consortium that took over Newcastle United in 2021, alongside Saudi Arabia's Public Investment Fund and the Reuben brothers. Within 18 months the club had qualified for the Champions League, and the foundations laid during that period contributed to last year's Carabao Cup win, Newcastle's first domestic trophy in 70 years.
The Reuben brothers, who remain co-owners at Newcastle, are not involved in the group exploring a move for West Ham.
West Ham's current ownership is led by majority shareholder David Sullivan, who holds 38.8%, alongside Daniel Kretinsky on 27% and the Gold Family Trust on 25.1%. Sullivan stepped down as joint-chairman and director earlier this month, shortly before allegations concerning his personal life became public.
West Ham were relegated from the Premier League on the final day of last season, leaving the club in need of fresh investment and direction as it prepares for life in the Championship.