Rapoport mentioned that the Cowboys had made it known that Griffen was available.
Todd Archer adds that the pick can become a fifth-round pick if the conditions are met.
Griffen is owed around half of his $6 million salary for the 2020 season.
Griffen, 32, is a former fourth-round pick of the Vikings back in 2010. He signed a six-year, $75 million contract that includes $34 million guaranteed in 2017, but the Vikings declined to pick up his option back in February, which allowed him to become a free agent.
The Cowboys signed Griffen to a one-year, $6 million contract a few months ago.
In 2020, Griffen has appeared in seven games for the Cowboys and has recorded 20 tackles, 2.5 sacks and a forced fumble.