According to the Evening Herald, producers are keen for the former Liberty X singer and her partner Hugh Hanley to take part with reality TV regulars Kerry Katona and Mark Croft.
However, it is believed that the current on-off nature of Katona's marriage has led to fears that a replacement couple may have to be signed up to appear with Heaton and Hanley in the show's latest celebrity special.
An insider explained: "Putting the two couples together on Wife Swap would have been great reality TV. They're all very high profile and are regularly in the news but they couldn't be more different.
"The plan was to bring Michelle over to Kerry's home and see how she coped with four kids and living with Mark. While Kerry, who loves nothing more than having a few drinks and a take-away, would come to Ireland and live with Hugh, who doesn't drink at all and eats really healthily."
Heaton has already appeared in Celebrity Big Brother this year and is currently making headlines as she stands by Katie Price throughout her current divorce dramas.
Asked to comment on the rumours, Hanley replied: "As regards Wife Swap, we can't talk about it but as soon as we can we will let you know."