Short answer: nothing in the wiki suggests Andy Reid or the Chiefs are in on Barkley — and the trade buzz that does exist makes a Chiefs landing spot unlikely.
Here's what's actually reported:
- Barkley is a likely trade candidate, but not to KC. With the Eagles at 1-5 and eliminated from contention (Hurts on IR, O-line collapsed), SI's deadline survey lists Barkley as a "maybe sell" piece (from the Saquon Barkley page). But the landing spots named are Minnesota (PFF's pick) and Seattle — not Kansas City.
- The math is a hurdle. Trading Barkley carries a $35M dead-cap hit for Philly, which PFF calls "a big hurdle" that only desperate contenders would absorb (from the Saquon Barkley page). That limits the realistic buyer pool.
- The Chiefs don't need him. KC already has Kenneth Walker III as their lead back, and there's no reported Barkley-to-Chiefs connection anywhere in the wiki.
So: Barkley could absolutely move before the deadline, but the reported destinations are Minnesota and Seattle. There's no evidence Reid is pursuing him.