That's an improvement from Friday when he said he was only at 40 percent.
"It's pretty good," Castro said. "I'm running hard. Good progress. [Tuesday] I'll run the bases."
Castro believes he might be able to get some at-bats in minor league games this week. Those games are in a more controlled environment. For example, he can leadoff every inning and play the field as little or as much as the Cubs want.
"He's doing very well," Renteria said. "We're very hopeful. He's moving in the right direction."
Castro has been out of the lineup since injuring his right hamstring on March 2. The Cubs believed he would miss 7-10 days but that's been extended.
Renteria and Castro believe he'll be ready for the regular season. Asked how many games he need to be ready, Castro said: "I think 8-10 games would be good. I think I'll be fine for Opening Day."