The Cowboys are in contract negotiations with Browns defensive coordinator Rob Ryan to take over that role in Dallas.
Ryan was defensive coordinator for the Raiders in 2004-08 but made the move to Cleveland two seasons ago.
Ryan is the twin brother of New York Jets head coach Rex Ryan and the son of former NFL coach Buddy Ryan.
Cowboys owner Jerry Jones removed the interim tag off head coach Jason Garrett Jan. 7 and is still looking for a defensive coordinator. The previous regime ran a 3-4 defense, and with most of the defensive personnel intact, Ryan fits the mold since he operates a similar scheme.
The Browns hired Rams offensive coordinator Pat Shurmur as their head coach Thursday and might be looking to move in a different direction on defense.