West Ham boss Allardyce last week admitted he expects New Zealand international Reid to leave Upton Park when his contract expires at the end of the season.
Arsenal have been linked with a move for the 26-year-old, but Allardyce, who is recovering from a chest infection that forced him to miss the 1-1 draw at Swansea City on Saturday, is determined to keep the centre-back unless a substantial offer is received.
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He said: "There's no choice for me, he stays - that's it. If somebody makes a big offer then obviously the chairman decides, but for me he’s staying.
"The chairman decides whether the money is big enough, but for me he stays and I think that the way the club has improved, I think he will stay.
"And I think that what we have done this season, and hopefully (we will) finish off the season strongly, might persuade him to sign for us.
"We are on the up at the moment and we have got a very big future ahead of us, moving into the new stadium. So the club could be bigger than it’s ever been in the next four to five years."
West Ham have been linked with a move for out-of-favour Manchester City defender Matija Nastasic, but Allardyce expects the Serbia centre-back to move abroad with Schalke reportedly closing in on a deal.
He said: "No I don't think Nastasic wants to stay in this country - that is my opinion based on the talks about Nastasic I had last summer before the window shut.
"The word was if he was going to leave Manchester City he wouldn't stay in this country."
Allardyce revealed that one or two of his players have "knocks and bruises" ahead of Tuesday's FA Cup third round replay with Everton but is hopeful that they will be available.
