Steelers general manager Kevin Colbert addressed Heyward's contract during an appearance Wednesday on The Fan Morning Show on 93.7 The Fan.
"When we have a great player, we always want them to finish their career here," Colbert said. "When that player has that same desire, it's usually something that can be worked out. We have another week prior to the regular season; we'll see where things go."
The 6'5", 295-pound defensive tackle is set to earn $9.5 million in base salary this season, the final year of a six-year, $59.2 million extension he signed in 2015.
Speaking to The Athletic's Mark Kaboly in June, the Pittsburgh native said he would like to continue his career with the Steelers beyond 2020.
"We [assume] something will get done, but assuming—I will always use that saying: If you assume, that makes an ass out of you and me," he said. "I have to be ready either way. I would love to be here for the rest of my career, and I feel I have plenty of good years ahead of me playing at a high level."
The Steelers selected Heyward No. 31 overall in the 2011 draft. The Ohio State product spent two years as a rotation player before being inserted into the starting lineup in 2013.
Since becoming a regular starter, Heyward has recorded 51.5 sacks and 29 pass breakups over the past seven seasons. He has been named to All-Pro first team twice (2017, 2019) and the Pro Bowl in each of the past three years.