Here are your Apple rumors and news items for Tuesday:

Tiny “iPad Mini” Rumors Get Big: Oct. 12, Brian White of Ticonderoga Securities said sources in China were hinting that Apple (NASDAQ:AAPL) was preparing a cheaper iPad device meant to compete with Amazon‘s (NASDAQ:AMZN) new $199 Kindle Fire tablet. He called it the “iPad Mini.” On Tuesday, a rumor originating from Taiwan’s United Daily News (via Mac Rumors) said component manufacturers AU Optronics and LG Display already possess samples of the new iPad, which sports a 7.85-inch screen with the same resolution as the current 9.7-inch iPad. In October 2010, former Apple CEO Steve Jobs indicated that Apple wouldn’t make a 7-inch screen iPad, describing other 7-inch tablets as “dead on arrival” technology.

Dropbox Turned Down Apple Offer: File storage startup Dropbox, an iCloud-like service, was rumored to be an acquisition target for Apple in September, but a new Forbes cover story on the company (via Mac Rumors) said the bid was more than a rumor. Dropbox founders Arash Ferdowsi and Drew Houston met personally with Steve Jobs and turned down an $800 million offer from Apple. Jobs apparently warned the duo of trusting private investors into their company.

Apple Preparing New MacBook Pros for November: Just in time for Christmas, Apple will release new models of its high-end MacBook Pro laptops. 9 to 5 Mac reported on Tuesday that listings on Apple’s online store popped up to support previous rumors that the new models were coming this year. Listings for the “MacBook Pro Memory Model” in the Apple store suggest the new laptops will ship in November. While not dramatic upgrades, the new models will include slightly more powerful CPUs and improved Bluetooth wireless networking.

As of this writing, Anthony John Agnello did not own a position in any of the stocks named here. Follow him on Twitter at @ajohnagnello and become a fan of InvestorPlace on Facebook.