It has been suggested that the Owls are among those considering an approach for a man being heavily linked with a move away from St James' Park.
Ameobi has slipped down the attacking pecking order at Newcastle and has just a year left to run on his current contract on Tyneside.
Alan Pardew has also admitted to being in the hunt for a new frontman this summer, which would further restrict the 31-year-old's first team opportunities.
Whether he does move on during the summer window remains to be seen, but Jones insists there is no chance of him ending up at Hillsborough.
He has been left bemused by some of the transfer rumours doing the rounds, with the Owls in no position to finance the kind of deals being discussed.
He told the Sheffield Star on the Ameobi link: "I don't know where people keep getting these names from.
"One minute it is Kenwyne Jones and the next it is Shola Ameobi.
"People keep linking us with players who are at clubs with far bigger wage bills than ourselves. It is absolutely ridiculous."