Benayoun has made just two substitute appearances for the Hammers since joining on a season-long loan deal this summer.
The Israel captain was surprisingly dropped by national coach Eli Guttman for this weekend's World Cup qualifying double header against Luxembourg due to a lack of playing time.
The 32-year-old told The Sun that he needs to play more minutes to take up an option to extend his loan in east London.
He said: "There is an option to extend my loan.
"My ambition is to be here for a full season and to make it a good one. It's great to be here but there's strength in depth."
Beanyoun has amassed a vast array of Premier League experience with a string of clubs, including Liverpool, Chelsea, Arsenal and a previous spell with the Hammers.