The blow-up animal famously halted flights around Heathrow after breaking free of moorings over London's Battersea Power Station in the 1970s.
Algie was swept away by the wind and was later recovered from a Kent field.
He was to be auctioned in an inflatable pop memorabilia sale next month, but has now been offered back to the band.
A picture of the floating pig, known as Algie, graced the cover of Pink Floyd's 1977 album Animals.
Algie was made in Germany but came to Suffolk with a huge tear after his flying adventure to Halesworth-based Air Artists, which made a new version in 1987 after Roger Waters had left the band.
Robin Harries, of Air Artists, said: "I made the new pig and I thought I'm not going to throw the old one away, even though it's been condemned, so I just kept it ever since.
"The auctioneers rather jumped the gun with the list I provided them and publicised the fact the Pink Floyd pig might be one of the lots.
"I thought I should offer it back to Pink Floyd and they do want to welcome it home again."
Beccles-based Durrants is hosting the online auction on 15 September and it still includes the second version of the pig, as well as items made for The Rolling Stones and AC/DC.
Algie's future remains uncertain but Mr Harries said there had had been "lots of talk" of a Pink Floyd exhibition.
He said: "Hopefully this pig will spur them on to get on with that."
Pink Floyd's inflatable pig "Algie" - which has been languishing in a Suffolk workshop for years - has been withdrawn from auction.