"I am confident that Danny and James will be staying with us," Wasps chief executive Tony Copsey told The Guardian.
"We have been talking to them regularly and, while there is no pressure on anyone, we would like to have the contracts dealt with by the end of the month.
"We are in good financial shape with Steve (Hayes) taking over the ownership and we are bucking the current trend."
Haskell was heavily linked with Northampton Saints last season, while Cipriani is seen as one of the most exciting players of his generation.
The pair both signed their previous deals before they reached international status, meaning that they are likely to be able to demand sizeable salary increases. The much talked about fly-half has since go on to win seven England caps, while back row star Haskell has made 12 appearances for his country.
Both youngsters played key roles in their club's domestic success last season but will be able to enter into negotiations with other teams if they have not committed themselves to Wasps before the New Year.
"Wasps has been and will continue to be about the people," said Hayes, who stepped up from Board member to club owner earlier this month.
"We want to ensure that we keep and attract the best players to ensure we maintain the success that has been seen over the last decade."