Manager Mike Scioscia said Wood could also see time at first base and shortstop as the Angels deal with the indefinite absence of Erick Aybar, who was hurt on a play at second base Tuesday night.
Wood, who was listed on the DL with a hip flexor strain, hasn't played since May 23 and was batting .156 with two home runs and seven RBIs in 122 at-bats. He played in 13 rehab games for Salt Lake and didn't fare much better there, hitting .196 with one home run and two RBIs. He had 17 strikeouts and three walks.
Scioscia used the term "secondary role" to describe what Wood could be headed for.
"You're always trying to play for at-bats and play for playing time," Scioscia said. "If you're not performing and not achieving, you look at a secondary role. So we'll see where Brandon is and how much he's contributing both on the offensive and defensive end and see what he needs to do."
Wood said Scioscia had not discussed his role with him of late, but he understands his production needs to increase.
"I'm trying to get back into a groove and get my swing back where it needs to be," Wood said. "You got to hit to be in the lineup every day." Wood made a mechanical change while rehabbing, bringing his hands lower in his stance.
Rodriguez made one appearance Monday night, throwing two innings and allowing one run on one hit and two walks. He struck out two.
"Right now we have an off-day on Thursday, so hopefully we can get through the next couple days with 11 pitchers instead of 12," said Scioscia, who added Rodriguez would not have been available Tuesday night.
"Sometimes it happens, like last year, I got called up like seven times last year," Rodriguez said. "Just be ready when they need me."