Jaramillo, 59, is believed to be at the top of the Cubs' list. He broke ties with the Rangers when the team offered a one-year deal for 2010, not a multi-year contract.
Cubs general manager Jim Hendry, who has been in Arizona meeting with staff, would not confirm or deny whether he's talked to Jaramillo, who has been the Rangers hitting coach since 1995.
"This is my decision," Jaramillo said about leaving Texas. "I want to go out there and see where I stand in the game."
Rangers hitters have won 17 Silver Slugger Awards, four Most Valuable Player Awards, three home run titles, and three RBI crowns under Jaramillo.
The Rangers led the Majors in runs scored in 2008, but dropped off a little in 2009. The Cubs also had a drop off from 2008 to '09. They led the National League with 855 runs scored in 2008 when they won 97 games, but finished with 707 this year and ranked 10th.
Gerald Perry began the year as the Cubs hitting coach, but was relieved of his duties in June and Von Joshua was promoted from Triple-A Iowa to take over. The Cubs had hoped Joshua could get Geovany Soto, Ryan Theriot and Mike Fontenot on track, but opted not to keep Joshua with the big league team for 2010. Joshua will return to the Minor League club as its hitting coach.
Carrie Muskat is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.