Darren Bent insisted he had to leave Aston Villa after too many "slaps in the face".
Brighton defender Greg Halford has agreed to extend his loan deal from Nottingham Forest until the New Year.
Diame, 25, has impressed at Upton Park since completing a free transfer from Wigan after running down his contract at the DW Stadium.
The Senegal international is reportedly attracting attention from a number of clubs and, although Allardyce refused to discuss a potential release clause in Diame's contract, Hammers co-chairman David Gold confirmed the fact on Twitter.
"Diame does have a release clause in his three-year contract. He joined us from Wigan on a free transfer," he wrote.
Allardyce would not be drawn on the speculation regarding the finer details of Diame's agreement, but did admit a big offer would leave the club "powerless" to stop him leaving.
"I don't disclose players' contracts publicly - there's always a situation where you're powerless to keep a player because of the size of the price," he said. "You can't turn it down - the chairman says, 'Look, we can't turn that down, Sam - we've got to move him on'."
With the January transfer window approaching, Allardyce compared Diame's situation to that of Swansea's Michu, who has also been linked with a host of clubs after his goalscoring exploits for Michael Laudrup's Swans.
He said: "I think there's always a chance that you lose football players when they start getting attention - because everybody is searching for better players.
"I'm listening to Mr Laudrup about how desperately they don't want Michu to go because January is nearly here and the rumours are starting again.
"All the agents are ringing you up and telling you that such a club is after this, and such a transfer is here and that club wants this player."
Diame's summer arrival was relatively low key at Upton Park in comparison to the club-record fee West Ham splashed out on England winger Matt Jarvis and the loan signing of £35million Liverpool forward Andy Carroll.
But Allardyce revealed the Reds had also been looking to make a move for Diame - something which convinced the former Blackburn boss he was signing a good player.
"I spoke to (former Liverpool manager) Kenny (Dalglish) about it - for me it just sort of made me feel so much better than I'd already felt when I signed him," he said.
"When you speak to Kenny and he says, 'yes, we were going to take him,' it gives you that little bit more these days, signing players on. It's a huge task in terms of what you have to go through and that process and then when you've done it you've got somebody of Kenny's experience backing up what your judgement is."