The first possibility came from James Kendrick of jkontherun earlier this month. According to Macrumors, he did not believe this, but explained it as being plausable:
"In the "totally unlikely to come true" department, yesterday I was told that Sprint will be getting the iPhone this summer. You heard that right, while rumors have long pointed to Big Red getting the iPhone this year, never has it been mentioned that Sprint would be selling the iPhone. I can't believe this is true, although the source has been reliable in the past and does work for Sprint." He also explained that a source connected to the Sprint company explained that it was coming to their services. According to this source, it would be coming in September-- the same time as the Verizon iPhone.
Moreover, a Techupdate post explains that a BestBuy employee "confirms" the iPhone will be going to Sprint. However, this is the most unreliable source. Best buy employees aren't usually reliable when it comes to Apple products, and if this were true, more than one source would have heard about it.
Sprint has been dying lately, and when the C.E.O. was asked about it, he said that they would love to have it, but did not confirm them getting it.
We will just have to wait and see what happens. If apple releases their device to all carriers, they will clearly have a monopoly on the phone market, so this does seem plausible. Stay tuned for more news.