New Zealand captain Reid has established himself as a key player with the London club since his move from Danish side FC Midtjylland back in 2010.
The centre-back is in the last year of his contract at Upton Park and West Ham have so far failed to agree fresh terms with the 26-year-old.
West Ham manager Allardyce knows Reid's future is out of his hands, but hopes an agreement can be reached to keep him at the Premier League club.
"It is not only a concern for me, but it is a concern for the owners," he said.
"There's been talk about Winston and his contract for a pretty long period now which is obviously not my responsibility.
"But hopefully, sooner rather than later, that will come to a conclusion and a positive one. I can only hope that is going to be a positive result in the end.
"It's not that he doesn't want to stay. It's about the financial remuneration and whether they can come to the right level and right give or take or negotiation that gets us to a point where he will say, 'yes'. That's always the hard bit.
"If we could tie him up tomorrow then I think the owners, particularly, and myself would like that and not have it lingering. It's always a difficult negotiation."
‘We were in Amsterdam, so I faked a toothache to go and see Crystal Palace in the FA Cup final. I couldn’t make the replay, though – the Stones worked it out’: Rolling Stones guitarist Bill Wyman feigned injury to watch 3-3 draw with Manchester United
‘Home truths needed to be spoken at Manchester United and Ruben Amorim has been brave enough to do that – the way he’s dealt with Marcus Rashford has been correct’ Former Red Devils star praises new boss
