The boss will be out of contract at the end of the season but, with the club supplying £15 million for their move to the Olympic Stadium, he has been warned ahead of negotiations
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Allardyce, who has been at Upton Park since June 2011, received a substantial bonus when the Hammers achieved promotion but Sullivan says that only level-headed requests will be sanctioned.
"At the end of the season, we will sit down with Sam," the West Ham chief told the Daily Mirror.
"If he wants to stay and is reasonable with his demands, he will stay."
West Ham recently agreed to up their funding for the move to the Olympic Stadium from £5 million to £15m, along with the government supplying a further £25m, to secure the club as main tenants for the ground - with a move-in date pencilled in for the start of the 2016-17 season.