Manager Bob Melvin also said just as much.
"Everything is on schedule at this point for him," Melvin said.
Anderson threw what Melvin deemed "a very aggressive side" in St. Petersburg on Sunday, and on Monday he said he was encouraged by how the ankle responded, though some more running drills later in the day gave him an even better indication of his progress.
"I can obviously feel it a little bit when running," Anderson said, "but other than that, it feels good."
Anderson, who will be opposed by Jon Lester on Wednesday, is 5-2 with a 2.70 ERA in eight career starts against the Red Sox.
Jane Lee is a reporter for MLB.com. Read her blog, Major Lee-ague, and follow her on Twitter @JaneMLB. This story was not subject to the approval of Major League Baseball or its clubs.