Quinn is owed $11.8 million in 2019 and carries a $12.9 million cap hit, per Spotrac. The team already paid him a $1.12 million roster bonus last week.
According to Armando Salguero of the Miami Herald, the Dolphins are willing to pay down the lineman's remaining contract to help facilitate a deal. The team is reportedly looking to acquire a draft pick in return.
In his first year with the Dolphins, the two-time Pro Bowler recorded 38 combined tackles, 6.5 sacks and two forced fumbles. He has piled up 15 sacks over the past two seasons.
The Cowboys are in the market for a pass-rusher after defensive end Randy Gregory was suspended indefinitely by the NFL in February. Gregory ranked second on the team with six sacks last season.
Miami is looking to build for the future, and Quinn—who turns 29 in May—does not appear to be part of the team's long-term plans as he enters the final year of his contract.
Pelissero noted Quinn would have to agree to any deal.