Hinds is out-of-contract at Glanford Park this summer and has been offered a deal to stay.
But the player has been offered more money to join a different club, and Adkins fears he will become the second first-team player to leave more money this summer.
Earlier this week Steve Foster chose to join League Two outfit Darlington after turning down United's contract offer.
"I have had a very good conversation with Hinds' agent, we want him to stay," Adkins told the Scunthorpe Telegraph.
"But there is another deal on the table that we can't get anywhere near from a financial point of view."