The Argentine forward has struggled for playing time since arriving in the close-season from Velez Sarsfield and revealed on Monday that he was in line for a move to Loftus Road.
Zarate hit out at West Ham and Allardyce in the British press, stating the 60-year-old refused to select him because he had been signed by the board.
The former Lazio striker also criticised Allardyce for showing him a lack of respect.
Asked whether Zarate was having a medical with QPR, Allardyce confirmed at his media briefing on Tuesday: "Yes, he is."
On the subject of whether he anticipated seeing the player leave on a loan deal, he added: "Yes, I would."
Despite ending the year with back-to-back defeats, West Ham go into 2015 sixth in the Premier League table ahead of their clash with West Brom on New Year's Day.
And Allardyce revealed his current campaign with West Ham - following a tricky season last time out - ranks among his best achievements as a manager.
"It's up there with revitalising Notts County after the only relegation I've ever experienced," he explained.
"We were champions the next year. Then at Bolton, I did a similar to job to here. We got promoted then struggled for a few years but after that we really pushed on.
"Years four, five and six were some fantastic years. We had cup finals as well as European places. So hopefully we're on a similar path at West Ham.
"We've invested in the squad and bought some young players in who will hopefully be here for a while and take the club to the next level."
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