The 25-year-old is the longest-serving player in the Hammers' squad having come up through the youth academy before making his debut in 2004, but his current deal expires next summer.
Allardyce is looking to avoid a similar situation that saw Rob Green's contract run down this year, before the goalkeeper left for QPR on a free transfer.
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"Talks have been ongoing since the end of last season," Allardyce told Sky Sports. "I would have thought they would continue until a conclusion is reached. Hopefully that conclusion will see him sign a new deal.
"He comes in every day and works hard and he is as happy as any player, particularly after our 3-0 win over Fulham.
"Every player at the club is in a good, positive frame of mind at the moment, so there is no hangover from him not renewing his current deal.
"I hope it doesn't get to that, we had a long, arduous contract negotiation with Robert Green which lasted an entire season.
"From probably about the second week I was here it started in Switzerland on the pre-season tour and we tried to negotiate all the way through to the very, very end of the last game at Wembley.
"I had one more go after that and we couldn't come to striking a deal so I jumped on the back that Jussi [Jaaskelainen] was available and wanted to come.
"So I hope it doesn't come to that situation, I hope that is something that can be resolved and he stays a West Ham player."