Rodriguez put in time at all four infield positions as well as in the outfield for Tampa Bay last year. He hit .211 in 237 plate appearances with 12 home runs and 41 RBI - both career bests - for the Rays last season.
In the last five years, all with the Rays, he has hit .228 with 40 home runs, 172 RBI and 32 stolen bases.
The 29-year-old is currently eligible for salary arbitration. He earned $1.48 million last year.
"Maybe a change is what's needed for me at this point in my career," Rodriguez told the Pittsburgh Tribune-Review. "I don't think I've reached my potential yet. I know I can do more."