St. Louis exercised a $16 million option for 2011 on Oct. 6 for the three-time NL MVP.
"I hope that before the season begins I get an extension," the 30-year-old Pujols said during a news conference Thursday.
The team has said there's no specific timetable for beginning negotiations on a new deal with Pujols, who can be a free agent after next year's World Series.
Pujols said he wants to spend the rest of his career with the Cardinals, "but that is something that I cannot control."
Pujols led the NL with 42 home runs, increasing his career total to 408, and won his first league RBIs title with 118. He batted .312, less than a percentage point behind team leader Matt Holliday.
He said it was his best season but was disappointed the Cardinals finished 86-76, five games behind the NL Central champion Cincinnati Reds.
"Personally it was a great season, but I feel bad because my team did not make it to the playoffs," he said.
Pujols also praised Mark McGwire, who just finished his first season as the Cardinals' hitting coach and agreed to stay on for next year.
"I believe that McGwire does not get the credit he deserves as the great batting coach that he is," Pujols said.