The striker has been linked with a move away from the Britannia Stadium in the January transfer window and allegedly sent manager Mark Hughes a text message on the eve of Sunday's match, which ended 5-3 to the Merseysiders, to inform him of his absence.
As well as being hit financially, Jones has been omitted from the squad for Saturday's trip to Crystal Palace.
"I was disappointed and Kenwyne has been fined because it is not something that should happen," said Hughes. "He won't be involved this weekend.
"We spoke on Monday, just to get an understanding of why it happened.
"We have had no contact from anybody for him this window, so maybe the information he is getting isn't correct.
"We're not looking to get rid of any striker. If we do, it will be on our terms rather than anyone else's."
Jones has scored five goals for Stoke this season, all in cup competitions.
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