The Bayern Munich front man, who was displaced in the first team by Mario Mandzukic last season, fuelled speculation that he could be off reports emerged that he had sold his home.
But there appears to be a twist in the tale, with Benitez preferring to sign Edin Dzeko instead.
Reports in Italy suggest that a deal for Gomez is expected to go through on July 10.
However, Dzeko, who was in and out of the Citizens first team last season has been tracked by Napoli for a while.
Edin Dzeko appears to be Rafa Benitez's top striking transfer target
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Though trying to hold onto Edinson Cavani is a priority of Benitez, Dzeko is his top striking target.
Benteke smashed 19 goals in the Premier League last term.
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