The 'Opposites Attract' singer and Epic Records chairman said that they would happily accept Simon Cowell's invitation to judge a second season of the Fox contest.
"I would love to come back," Reid told People. "What I don't like is, I love it so much. I don't control it, it's up to the boss."
Abdul, meanwhile, said that she would be back on The X Factor "unless something weird and bizarre happens" before next season.
The pair's co-judge Nicole Scherzinger suggested earlier this week that she might quit The X Factor to focus on her music career.
"[The show] has been quite a learning experience, quite a journey for me," she said. "I didn't expect to have been so emotional through the whole elimination process. I wanted to just mentor and empower artists."
X Factor host Steve Jones is rumoured to have already been axed by producers, with Cat Deeley apparently being lined up to replace him.
Melanie Amaro was announced as X Factor USA's first winner on December 22.