Reports suggest that the Owls are keen on adding the Nigerian international to their frontline, with it looking increasingly likely that the forward will leave St James' Park this summer.
However, Jones insists that Ameobi will not be plying his trade at Hillsborough next season due to their financial restrictions.
"I don't know where people keep getting these names from," Jones told the Sheffield Star.
"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."
Ameobi has one year left to run on his current contract with Newcastle.