The 49ers definitely want to move on from Brandon Aiyuk — GM John Lynch said a split is "inevitable" and they've already signed Mike Evans and voided Aiyuk's guarantees. But a trade specifically is basically dead in the water.
As of late June, ESPN's Jeremy Fowler reported Aiyuk is "essentially untradeable right now" because he's on the Reserve/Left Squad list and hasn't even filed for reinstatement with the NFL (from the Brandon Aiyuk page). Until that happens, the 49ers can't trade or release him. Once he's reinstated (expected to be automatic), he can report to camp and force his release, at which point he'd likely sign for a veteran minimum rather than the $120M deal he once wanted.
The Commanders and Falcons are both interested if he hits the open market.
What the experts are saying:
Underdog Fantasy — Josh & Hayden think the longer the 49ers wait, the more likely Washington offers just a seventh-round pick to facilitate a trade, which would at least help San Francisco financially.
Sal Vetri — Notes Aiyuk is "obviously linked" to Washington because of his close friendship with Jayden Daniels from their Arizona State days.
Establish The Run — Calls the whole situation "a disaster" — not just the injury, but the bad-attitude reports and contract-void drama.
Bottom line: Don't expect a trade. A post-release signing by Washington or Atlanta is the most likely outcome once Aiyuk files for reinstatement.