Shakhtar president Rinat Akhmetov said on the club website: "Paulo Fonseca is at Shakhtar and I'm delighted with that".
Benitez has performed a remarkable job at Newcastle over the past campaign, leading them to a 10th place finish in their first season back in the Premier League.
"But he would probably look at West Ham's squad and think "there's a lot more potential in this squad".
Guillem Balague says Arsenal are interested in Rafa Benitez
A West Ham statement on Thursday said the club was "extremely confident of appointing a high-calibre first-team manager, who has a proven record both in the Premier League and European football".
Benitez has become a fan favourite on Tyneside and has also won admirers elsewhere.
Despite his frustrations with owner Mike Ashley and the board, there were not any direct connections to other Premier League options.More news: Varanasi flyover collapse: Prime Minister, VP condole deaths
It was in July of final 12 months that Benitez urged Ashley to "preserve his phrase" over switch funds and reminded him that he might have stop the membership for a mega-money deal in China.
It was in July of a year ago that Benitez urged Ashley to "keep his word" over transfer funds and reminded him that he could have quit the club for a mega-money deal in China.
Whether that budget will be enough to convince Benitez to stick around remains to be seen.More news: Reuben Foster's ex falsely accused another man of domestic violence in 2011
However it serves to focus on Benitez's frustration that such a state of affairs has been talked about since final summer time. A win-win scenario for him by capping us with a smaller turnover providing smaller outlays but expecting the greatest income.More news: Sonam Kapoor's Husband add wife's name in his surname
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