West Ham boss Slaven Bilic revealed Payet had gone on strike last week in a bid to push through a return to French club Marseille in January.
Payet missed West Ham’s 3-0 win over Crystal Palace and was widely expected to leave the club.
But Sky Sports say Marseille have now abandoned plans to sign Payet and are moving on to other targets.
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Dimitri Payet could be set to stay at West Ham
Dimitri Payet pictured training with West Ham under-23s
Wed, January 18, 2017
Dimitri Payet has been pictured training with West Ham under-23s
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Dimitri Payet has been pictured training with West Ham under-23s
West Ham have rejected bids either side of £20million for the France international and were set to return with an offer nearer £25m – despite the player’s £30m-plus valuation.
Payet has rejected offers of up to £500,000-a-week to head to China and is ready to accept a pay cut in order to return to his homeland, having complained of being homesick.
Marseille held talks with West Ham this week but the clubs failed to reach an agreement with their valuations differing by as much as £10m.
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Dimitri Payet is desperate to leave West Ham
Sky Sports reporter Kaveh Solhekol said: "I'm being told Marseille are resigned to not signing Dimitri Payet from West Ham during this window.
"Marseille do not think it will be possible to sign him during this window and they will be moving on to other targets this month. They have almost given up on signing him this month.
"There are two ways you can look at this and the first is that you can take what they are saying at face value.
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Slaven Bilic revealed Dimitri Payet went on strike at West Ham last week
"Another way of looking at it is this could be a game of brinkmanship with West Ham. West Ham have a player who is refusing to play and who is training with the U23s.
"They are demanding £30m and Marseille are not willing to pay more than £25m so is this just a game of poker between the clubs?
"Marseille are saying they're not going to pay that. What I'm being told is they're resigned to not signing him in this window."
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