Cumberbatch plays a contemporary Sherlock Holmes in BBC series Sherlock, while Miller will play a similar role in new CBS drama Elementary.
"I wanted to assure him that it was a different enough project," Miller told reporters. "He was excited for me and he was very encouraging and we discussed it."
Miller - who will star opposite Lucy Liu (Joan Watson) in Elementary - described Holmes as "a wonderful character to play".
"[Benedict] wanted to pass a lot of that on," he explained. "We discussed that for a bit, yeah. It's a strange one."
At this year's San Diego Comic-Con, Miller insisted that Cumberbatch is "very supportive" of Elementary.
The series will premiere on September 27 on CBS.
> Elementary Comic-Con 2012 panel - in full
Watch a preview of Elementary below: