Cole, Matthew Taylor, Jussi Jaaskelainen, Jack Collison and George McCartney will all see their contracts expire in the summer, but Allardyce has insisted that it is not the time to be entering negotiations with agents as the Hammers edge closer to Premier League safety.
"Joe will have to wait and see at the end of the season like five or six others, we will decide if and when we are safe," Allardyce revealed to reporters in his press conference ahead of Saturday's match against Manchester United.
"Is Joe happy to wait? He's got no choice, has he? He's contracted to us. Like all the others, the agents ring us up all the time, but if I start with one, then I'll have to do everybody.
"At this stage of the season, the last thing I want to do is be distracted by agents or contracts and talking about money."
Cole has recently been linked with a move to Championship club Brighton & Hove Albion.