Ohio Gov. John Kasich -- The Cavs Should Sign Allen Iverson!

The rumors have been swirling for months -- but now Ohio Gov. John Kasich tells TMZ Sports he hopes the Cleveland Cavaliers make it a reality ... and SIGN ALLEN IVERSON!!!!

Iverson is 40 years old ... and hasn't been in the NBA since 2010 ... but for some reason, the A.I. to CLE rumors have found a life on Twitter, despite the fact they're completely unfounded.

Still, Kasich says he's all for it -- "I'd love to have Iverson back in Cleveland ... wow A.I.!!!"

Iverson retired in 2013 and his jersey was retired in Philadelphia last year -- but, Jordan came back once, right??