The iPhone-Bing search rumor is back in circulation again today, with the Wall Street Journal, Silicon Alley Insider and BusinessWeek quoting Collins Stewart analyst Sandeep Aggarwal saying in a note that there’s a high likelihood Microsoft will secure a deal to make its search engine the default on Apple’s popular device.

Aggarwal, who previously worked inside Microsoft, based the comments on a visit with company executives in Redmond earlier this week, so the information seems solid. That raises the question: How much, exactly, would Microsoft be willing to give up for an iPhone search deal?

As we noted last week, Microsoft has already been paying large sums to boost Bing’s market share — with "traffic acquisition costs" increasing the cost of revenue in the company’s Online Services Division by 50 percent in the last quarter, to more than $500 million. Microsoft has made a series of deals to make Bing the default on PCs from companies such Dell and HP, and it reportedly paid hundreds of millions of dollars for a search deal with Verizon.

The company’s efforts have been paying off in higher market share, now more than 11 percent in the U.S., according to comScore. But so far that higher market share hasn’t translated into bigger profits in the division, with the loss actually widening last quarter.

Given the iPhone’s market share, and disproportionate Internet use among its customers, it’s no surprise that Microsoft would be eying a deal with Apple. It would no doubt help boost Bing’s market share. But depending on how much Microsoft pays for the deal, there’s no guarantee that the deal would have a similar effect on the company’s profits.

Aggarwal says in his note that Microsoft seems ready to do a deal with Apple as long as it’s for the "right economics."