"It's definitely better than it was, but it's still there," Lee told reporters on Monday. "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."
Lee, who is 4-4 with a 3.18 ERA this season, was diagnosed with a Grade 1/Grade 2 strain of his left elbow and was placed on the disabled list last week.
"It's the first time I've had anything like this, and obviously I was hoping for the best," he told reporters. "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, who will turn 36 in August, spent time on the disabled list in both 2007 and 2010 with abdominal strains and missed about three weeks in 2012 because of a strained oblique. But this is the first time in either his major league or minor league career that he's been placed on the DL with any type of arm issue as he has pitched 1,401 2/3 innings since 2008.
Lee's contract pays him $25 million this season and $25 million next season. He has a vesting option for $27.5 million in 2016, or a $12.5 million buyout. He also has a limited no-trade clause that allows him to block deals to 20 teams.
"It's pretty obvious what it is," Lee told reported on Monday. "I'll continue to work on it and let it heal. If it felt good today, it was going to be another week or so and hopefully come back after the 15 day [disabled list stint]. Now it's going to be a little longer."
Jayson Stark of ESPN.com and The Associated Press contributed to this report.