The 28-year-old, a free agent after being released by Midlands rivals Leicester this summer, caught the eye as he played just over an hour of the Rams' opening pre-season fixture at Burton on Saturday.
"We were very pleased with what we saw from Patrick for around an hour. It is well documented that centre-half is a position we are looking to improve and he may well be an improvement on what we have got," said Rams boss Nigel Clough.
"He has got Championship experience and although he is not 6ft 3in or 6ft 4in, he competes well and he can play full-back as well so it covers us in that position. We will sit down and have a chat with him."
It was Kisnorbo's goalbound header that Chris Porter glanced home for the only goal of the game at Burton and the centre-half crashed another header against the crossbar early in the second half.
Several clubs are interested in signing Kisnorbo, including Crystal Palace after he trained with them last week.