Pence didn't make his season debut until mid-May because of a broken left forearm sustained during spring training, and the right fielder has not played since June 2 because of a sore left wrist. San Francisco could make a DL stint retroactive and Pence would be eligible to be activated June 17.
"He was fine that day, but yesterday he showed up and was a little dizzy," Bochy said. "So he went through some tests, and that's where he's at because of the tests."
Blanco is batting .278 with one home run and seven RBIs in 48 games.
"We are optimistic right now that he will be ready to go on Tuesday," Bochy said.
Parker, a second-round draft pick of the Giants in 2010, spent one day with the Giants last August — also at Citi Field — and was optioned to Triple-A Fresno without making an appearance.
"Parker gives us a true extra outfielder," Bochy added. "He can play all three positions."
He was batting .268 with 12 home runs and 36 RBIs in 54 games with Sacramento.