If you find an object with no obvious owner, you either leave it where it lies, or you report it by turning it in somewhere. To the business where you found it, or the Lost & Found department of the transit authority, or the police if all else fails.
I don't see anyone calling up the police to say, "Hi, I found <item> and I'll keep it until someone comes over here to claim it!" because the only people coming over will be the police themselves.
Every place with a Lost & Found service, and the police, regularly liquidate the unclaimed property. You can find lists and auctions on your civic website if they're selling the stuff. They may also donate it to charity or destroy it.
The police or anyone else are not going to stick a tag on a box with your name and number so you can come to claim it after the grace period elapses. That's not how claiming stuff works.