"The dialogue has increased. The level of urgency is high on both sides. Let's go, Kevin Demoff," McVay said Tuesday.
Donald has not played the entire preseason while holding out for a new contract. He is due to make $6.9 million in the fifth-year contract option for 2018.
ESPN's Adam Schefter reported in July that Donald was not planning to play until he reached an agreement for a new contract. The Rams have handed out long-term contracts to Brandin Cooks, Todd Gurley and Rob Havenstein this offseason. They also signed Ndamukong Suh in free agency, further complicating matters with Donald.
Rams COO Kevin Demoff said on SiriusXM Radio that the team doesn't "see eye-to-eye on it right now" with Donald's representation.
"I think this is one of those situations where you have a great player who's played at historical levels through his first four years," Demoff said. "For us, it's trying to find the right balance to reward Aaron at a historical level, putting him among the elite players in the game where he deserves to be, while also preserving the fact that this is the second-youngest team. We're growing, we have a quarterback coming up who's eventually going to get paid, and making sure that we can keep this team together."
Donald is arguably the best defensive lineman in football. He recorded 41 tackles and 11 sacks in the 2017 season, winning the Defensive Player of the Year Award while earning his fourth straight Pro Bowl berth.
Over his first four seasons, Donald has recorded 39 sacks and missed just two games. McVay says if a contract gets done soon, he could still be in the lineup for Week 1.
"Hopefully if we do get it done in the next couple days, we do feel good about him being ready for Oakland," McVay told reporters.