Cueto remains in his native Dominican Republic while tending to his ill father, a week after pitchers and catchers reported to the Giants' camp in Arizona.
Giants manager Bruce Bochy had what he called a "great talk" via FaceTime with Cueto on Tuesday. "We got his schedule mapped out," Bochy said.
Cueto is continuing his throwing at the team's academy in Boca Chica, and Bochy said the pitcher is working to secure all the paperwork for his father to come with him to the United States.
Cueto, who signed a $130 million, six-year contract before last season, went 18-5 with a 2.79 ERA and five complete games in 32 starts last year.
"The WBC is starting to cause a slight concern," Bochy said Monday. "He'll be smart enough to know if he's ready or not."
Bochy said the 31-year-old Cueto ideally would be built up to the range of 50-60 pitches ahead of the World Baseball Classic. The Dominican squad is set to open against Canada in Pool C on March 9 in Miami.
Cueto showed a year ago in his first spring training with the Giants how meticulous a routine he keeps to prepare for a season and even between starts.
"You know Johnny: He's smart. He has a great way of getting ready, he paces himself," Bochy said. "You saw last year. ... Johnny knows what it takes to get ready."
If Cueto doesn't feel quite ready by March 9, there's also the option that he could join the Dominican Republic team for a later round of the tournament.
"We're fine. This spring has started early, so he'll have plenty of time to get ready," Bochy said. "Now the question will be, will he be ready for the WBC? That's the question we have to answer now, and that's why we're going to call him, we're going to try to get ahold of him to see exactly where we're at.
"He'll be honest with us. We're going to talk about a lot of things, see exactly where he's at, where he's at mentally, too, how his father's doing. He's got a lot going on right now."
Information from The Associated Press was used in this report.