It looks like Apple's as-of-late troubled relationship with Google isn't getting any better. Citing "two people familiar with the matter," BusinessWeek reports that the Cupertino based company is shopping around for a search engine alternative to Google on the iPhone, and has supposedly spent "weeks" discussing a deal with none other than long time operating system rival Microsoft.

If true, the deal would give Bing a much-needed market share boost in the mobile sector. Apple would benefit too, as Microsoft would likely offer a higher cut of the mobile advertising profits than the company currently receives from Google to seal the deal. Of course, there is some concern that this could annoy iPhone users who like things just as they are, but the deal doesn't discard the option for them to manually switch search providers.

The magazine also said that Apple is looking at providing a search option itself eventually and that a deal with Microsoft may be "about buying itself time." Not so long ago the company also purchased a mapping software firm, suggesting that the Google Maps iPhone app could be on its way out of the default software bundle.