Lee has a Grade 1/Grade 2 strain in his left elbow and was placed on the 15-day disabled list last week.
Lee, 35, is 4-4 with a 3.18 ERA this season for the Phillies.
"It's definitely better than it was, but it's still there," Lee said, via the South Jersey Times. "It's a real small spot right on the edge of the bone where the flexor tendon attaches. When I have to turn (my arm) I can feel it.
"No sense in rushing it."
It's the first time I've had anything like this, and obviously I was hoping for the best," Lee said. "They did a couple tests and I can still feel it a little bit. They decided to have me wait and when I have no symptoms, I'll start throwing. I pretty much agreed with that, it makes sense. There's no sense in throwing if I can still feel it doing some of the tests they had me do."
Lee is owed $25 million each for this season and 2015, part of a five-year, $120 million contract he signed in 2010. The deal includes a $27.5 million vesting option for 2016 with a $12.5 million buyout.SI.COM STAFF: Phillies No. 27 in this week's MLB Power Rankings