Grant has spent the past two weeks with his father in Australia, where the funeral is scheduled for Friday.
Rays manager Kevin Cash talked to Balfour Wednesday morning.
"The tentative plan is [for him] to fly in Saturday night and be with us Sunday morning," Cash said. "Obviously, that's what he's booked for, but we'll wait and see how the flights come out. It sounds like it should work."
Cash said Balfour "seemed OK" given the circumstances.
"I mean, he's got a lot on his plate," Cash said. "Not only did his dad pass, he has to organize a lot of the services, so he's got a ton on his plate. Hopefully in the back of his mind, where it belongs in the back of his mind, he's thinking about getting ready for his season.
"He said he threw a bullpen today -- his today -- when we talked earlier this morning. That's just a lot for what he's been going through the last couple of weeks. ... Grant seemed clearly motivated to get back, maybe a little more just watching how his dad fought there at the end."
Hearts went out to Balfour in the Rays' clubhouse on Wednesday.
"He's been going through a lot the past couple of years," Jeff Beliveau said. "Just talking to him about it last year, he said it's been tough dealing with his dad having cancer. Kind of like beating it once and then getting it back and dealing with it again. We're all with him. Our best goes out to him.
"It's tough. I can't even imagine having something like that with your dad on top of all the other stress and other issues we have going on in our lives. And his is halfway across the world. So he has to go back there and deal with what he has to deal with. And our best just goes out to him. It's just really sad to hear."
Long-time bullpen catcher Scott Cursi mentioned how Balfour arranged to have his father on a team charter to New York last season.
"I had the opportunity to talk to him and he was a great guy," Cursi said. "I didn't know that he was sick until the end of the year last year. He looked normal to me. Tremendously fun guy. My heart goes out to Grant, and the family."
In December, Balfour told MLB.com that being around as his father battled cancer had added a lot of perspective to Grant's own life.
"Seeing what he's going through, you see some things differently for sure," Balfour said. "He's been fighting for a while. We try to fight it with him, but he's doing all the work. He's going through all the aches and pains.
"At the end of the day, health is No. 1. If you have a healthy family, it doesn't get much better than that."
Bill Chastain is the Rays beat reporter for MLB.com. He has been covering the club since 2004. This story was not subject to the approval of Major League Baseball or its clubs.