Allardyce has helped West Ham become one of this term's surprise packages in the Premier League, having come in for criticism from sections of the club's support last season.
The Upton Park outfit could end the year in the top four but doubts continue to linger over Allardyce's future, with his contract expiring at the end of the season.
Sullivan feels his usual rule of not negotiating contracts with managers until the season is over may come back to haunt him and hinted he may break with tradition in this case.
The West Ham chief told The Telegraph: "I must say if come April we are where we are now [in the Premier League table], which is extremely unlikely but is possible, we'd probably sit down a month early and say 'Look Sam, do you want to stay or do you want to go?'
"Sam may decide he wants to go out a winner. He may decide, after four years, it's a very stressful job, he may decide he wants £10 million-a-year, which we can’t afford.
"All I will say is we don’t have a contract in a draw with another manager. We will sit down with Sam and see if it makes sense for both parties.
"We are very open and honest. We have always said that to Sam and he’s very happy with it.
"Sam is very confident in his own ability. He’s confident he could get another job so he’s always happy to negotiate at the end of the season or late in the season, which has always been our strategy."
