Jenkins had a physical examination with the team doctor on Monday.
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There have been no changes with the safety's current deal. But talks are ongoing with the team, according to the source, and "heading in a direction that now has him committed to attend" camp.
A source confirms this information with ESPN's Adam Schefter.
According Schefter, Jenkins is said to be excited to be with his teammates and focused on the 2019 season as an Eagle.
Jenkins skipped the team's offseason workout program and was a no-show for voluntary organized team activities.
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As ESPN's Tim McManus reported, It appeared to be understood within the locker room that his decision to stay away is contract-related.
"We need him," defensive end Brandon Graham said. "I know [executive vice president of football operations] Howie [Roseman] and them, they're going to take care of their business. At the end of the day, you've got to take care of your business no matter what, because when you're on that field, you've got to make sure you cover yourself as a player, and obviously they've got to cover themselves as an organization. We all have to handle our business. Business-mind first, play later."
Jenkins, 31, has two years remaining on the four-year, $35 million extension he signed in 2016.
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ESPN contributed to this report.