Raul Ibanez says even he rolls his eyes on occasion when he reads about players vowing to produce big years. But Ibanez, who remains a free agent, is confident that he will bounce back strong, even though he turns 40 on June 2.

The reason: A revelatory three-day session that Ibanez had in December with Cubs hitting coach Rudy Jaramillo.

“It took him every bit of about 20 minutes, and he completely changed what I was doing,” Ibanez says. “I consistently produced line drives, over and over again. He simplified everything for me.

“The last two years, I was trying to do 200 different things at once. Now I’ve got three different checkpoints. Every time I take a swing that is not right, I go to those three things.”

Ibanez says he also worked with Jaramillo before the 2002, ’08 and ’09 seasons. The two did not work prior to ’10, when Ibanez was recovering from surgery to repair a sports hernia. And last offseason, Ibanez says he went, “in a totally different direction, doing some other stuff that didn’t work out.”

Ibanez finished with a .289 on-base percentage, his lowest since 1998, and a .419 slugging percentage, his lowest since ’99. Two awful slumps — an 0-for-35 and a 5-for-44 — contributed mightily to his disappointing numbers with the Phillies.

Still, Ibanez finished with 32 doubles, 20 home runs and 84 RBI. It was his 10th straight season of 30 or more doubles. He has reached 20 homers in six of his last seven seasons, 80 RBI in nine of his last 10.

“I know 2012 is going to be way better than 2011,” Ibanez says. “I didn’t know quite how I was going to do it. But I knew I was going to do it.

“Now I expect that (2012) is going to be great. That’s the different level I went to. I haven’t felt this good since I left for spring training in ’09 — the last time I worked with Rudy.”

Ibanez, who lives in the Miami area, says he plans to visit Jamarillo in Texas on Tuesday for a “touch-up” session.

The Yankees, in need of a DH, are one possible fit for Ibanez, who was a teammate of Alex Rodriguez’s in both the minors and majors with the Mariners and became close with Yankees hitting coach Kevin Long when the two were together in the Royals’ organization.

— Ken Rosenthal