The Daily Star report that QPR boss Mark Hughes has joined Arsenal in the chase for the Argentine striker.
Lazio are reportedly prepared to sell Zarate for around £10million.
Zarate is currently on loan at Inter Milan.
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.