A fee of £500,000 was agreed, but the transfer stalled on personal terms and now the Championship club say they have ended their interest in the player.
"The clubs agreed a fee and myself and my agent spoke to Sheffield Wednesday's representatives but unfortunately it didn't work out and I'm more than happy to stay at Tranmere," said Hume.
"I spoke to (Rovers manager) Brian (Little) and he said he wouldn't hold me back if the chance came to move up because unfortunately it didn't happen with Tranmere last season.
"If the opportunity came up again and the club were getting the right fee for me, obviously I'd have to think about it again but I've got a lot of history at Tranmere and it would have to be the right package for me to consider leaving somewhere that I'm very happy."
Rovers boss Little added: "It was a good offer but whatever happened, happened and we're glad that Iain's still our player."