The French midfielder was part of the starting side which helped the Blues reclaim the FA Cup against Everton on Saturday - his first trophy since his £13.5 million switch from Lyon in 2007.
It represents a remarkable turnaround in fortunes for the 28-year-old, who has been transformed from a fringe player under Luiz Felipe Scolari into a first-team regular by temporary boss Guus Hiddink.
New manager Carlo Ancelotti is now expected to offer him a two-year extension to his current deal, which has a year to run.
A delighted Malouda told the London Evening Standard: "We will have a meeting at the beginning of June. Both parties want to carry on.
Wonderful experience"It's a wonderful experience but just the beginning. I hope in the next years you will see me win many, many trophies.
"When you play so many high-profile games you get the experience and confidence that comes with it. I hope to share joy and happiness with the fans."
Malouda is expected to face more competition for his place on the left of midfield next season if Yuri Zhirkov arrives from CSKA Moscow, although the Russian international insisted on Wednesday that Chelsea had not made an approach for his services.
Asked if he is ready to compete with Zhirkov should he arrive, Malouda replied: "Of course. It's just the beginning because with Ashley Cole left we have confidence so it gives us a lot for the next years."
Defender Alex is also expected to rewarded with a new three-year deal to keep him at the club, as is striker Didier Drogba.