The 29-year old, whose current deal is set to expire in the summer, has been ever-present for the Eagles so far this season having joined from Turkish side Genclerbirligi in 2011.
Jedinak had been in negotiations with Palace since the start of the season and despite the exit of former boss Ian Holloway last month, Millen believes that both parties are edging nearer to a resolution.
"It's not been signed yet but I think it's almost agreed," he told London24.
"Mile's been a great servant to the club. He's a captain, he's a leader and we want him to stay. We know he's happy at Crystal Palace."
The Australia international maintains that he intends to remain at Crystal Palace, but admits that he may need to be patient before negotiations are completed.
"I do want to stay in the Premier League and I do want to stay at Crystal Palace," Jedinak explained to The Daily Examiner.
"It is what it is at the minute. Only time will tell."