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.
Dave Jones: "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."
Ameobi has one year left to run on his current contract with Newcastle.
WE TELL IT AS IT IS - NO BULLSHIT!
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Rio Ave (A) July 20
Pacos Ferreira (A) July 23
Blackpool (A) July 29
St Mirren (A) July 31
Braga (H) August 10
MOTHERWELL 2 NEWCASTLE 4 (Vuckic, Gouffran, Sissoko, Marveaux)
Elliot; Tavernier, Williamson (S Taylor, 46), Yanga-Mbiwa (Streete, 82), Dummett; Sissoko (Abeid, 68), Anita (Amalfitano, 82); Obertan (Ferguson, 74), Vuckic (Marveaux, 46), Sammy Ameobi (Richardson, 82), Gouffran (Campbell, 58).
Sub not used: Alnwick.