The Hammers' manager revealed the club cannot prevent the Senegal international from leaving due to a release clause in his contract, with thje Gunners reportedly interested
The Senegal international has been a revelation since moving to Upton Park in the summer on a free transfer, but Goal.com exclusively revealed Arsenal will move for him in January as his release clause is "close to £4 million."
And while the Hammers' boss would love to keep the combative player in his side, the clause means a host of clubs may attempt to snap up Diame in the approaching transfer window.
"There is always a situation where you are powerless to keep a player. Because of the size of the fee, you can't turn it down and the chairman says, 'We can’t say no, we've got to move him on'. But I won't be disclosing a player’s contract," he told reporters.
Allardyce suggested the contract was one of the main reasons why Diame joined the east London club - and also revealed the player could well have joined Liverpool had Kenny Dalglish not been sacked.
He continued: "I didn't really ever have to convince Mohamed to join West Ham, it was all about the contract. In the end, it took a bit of time, but we came to a financial agreement that was suitable for the club and the player.
"I spoke to Kenny about signing Mo. For me, it just made me feel so much better than I already felt about signing him, to have Kenny saying 'Yeah, we were going to take him'."
The 58-year-old suggested Diame's contract stand-off with Wigan coupled with their fine late-season form meant the midfielder did not feature heavily at the DW Stadium, but has now found a new home: "Last year, at Wigan, Mohamed didn't play as often. In the beginning, it was the refusal to sign a new contract and wanting to see it out.
"Then, at the latter end of the season, Wigan did very well and didn't need him. In the end, that worked to our benefit."
And Allardyce stated the January transfer window always brings uncertainty as clubs look to cherry-pick the best performers of the season so far, with Diame clearly a target for other Premier League clubs: "There is always a chance you will lose football players when they start getting attention, because everybody is searching for better players.
"I am listening to Michael Laudrup trying to keep Michu at Swansea because January is nearly here and all the agents are ringing him up.
"All that distraction starts now and doesn't finish until January 31, when the transfer window is closed. That’s why we should all have a break," he added.