Tanaka, 30, took a 111.3-mph ball off his shin in Saturday's 2-1 loss to the Tampa Bay Rays. He left after six innings with a shin contusion.
"I would say today was at least encouraging that he walked in feeling pretty well," Boone said, according to MLB.com. "Definitely some soreness in there, but walking is not an issue."
Tanaka was caught screaming in pain as he left the mound. X-rays were negative.
Boone said the Yankees will make a decision on Tanaka's status after he throws this week. Tanaka is next slated to take the ball against Baltimore on Thursday afternoon.
"I think there's a chance he'll make the next start," Boone said. "That would be the hope."
Tanaka is 3-3 with a 3.09 ERA in 10 starts this season. He is on pace to finish with his lowest ERA since posting a 3.07 mark in 2016.