The chief executive of Bridge Oracle, Mr Estavi, had claimed that he had been offered $10m for the message.
The highest bid was $6,222.36.
Mr Estavi told the radio station that he may never sell the tweet unless he received a high bid.
Last year, when I paid for this NFT, very few people even heard of it. The NFT is the epitome of the digital world. Mr Estavi said that there is only one of that and it will never be the same.
The value of the NFT will be realised years later, he said.
Mr Estavi was the buyer of Mr Dorsey's brief tweet, which was sold on an online platform called Valuables, which is owned by the US-based company Cent.
As the buyer, Mr Estavi received a certificate, digitally signed and verified by Mr Dorsey, as well as the original tweet.
The data includes the time and text of the post.
Although Mr Estavi is looking for a buyer, he won't accept anyone's offer.
I think the value of this NFT is far greater than you can imagine, and whoever wants to buy it must be worthy.
Mr Estavi said that someone like Musk could be deserving of the NFT.
NFTs that are one of a kind have often been sold for a lot of money.