So reports Reuters, citing a source “familiar with Yahoo (NSDQ: YHOO) management’s thinking”. It says that Yahoo “insiders” are mulling ties with rival Google (NSDQ: GOOG). Industry observers have been asking Yahoo to consider outsourcing its search to Google for a while now, and this might be the thinking here. Also, Yahoo believes Microsoft’s (NSDQ: MSFT) $44.6 billion offer undervalues the company.

Update: Staci adds: WSJ reports that Eric Schmidt called Jerry Yang Friday to offer Google’s help thwarting Microsoft’s bid. The Journal adds: “People familiar with the matter say Yahoo’s board of directors, which conferred by telephone Friday, hasn’t taken a position so far and no rival bids have emerged yet, though it remains possible some will.”

So what could Google do given the regulatory issues involved in any direct acquisition? “… People familiar with the matter say Google could play a role in attempts by others to outbid Microsoft, or by Yahoo to remain independent. Google could potentially offer money, or guaranteed revenue in return for a Yahoo advertising outsourcing pact, under that scenario, say people familiar with the matter. Even such involvement by Google would likely attract antitrust scrutiny because of concerns that competition between the two Silicon Valley Internet companies could be reduced.”

The Journal also reports that Yahoo and Google were already in negotiations about outsourcing the former’s search advertising in Europe—and that those negotiations will continue despite the bid. Yang so far has resisted outsourcing part or all of Yahoo’s search advertising. We reported Yahoo considering outsourcing European search last year.

As for potential rivals, so far lots of storm and fury signifying nothing. One person I spoke with over the weekend, who is familiar with previous approaches to Yahoo, raised two points against a major rival bid: One, Microsoft’s determination and deep pockets, and 2) when it comes rumors of private equity money, the difficulty of raising $25 billion—his estimate of the minimum it would take—in a brutal debt market.