The entreaty appears after executing a search from google.com in Firefox when the browser has Yahoo as its default provider.
"Switch your default search engine to Google," the alert stated. When users click the offered "Learn how" button, they see instructions for changing the provider.
Search Engine Land first reported on Google's request.
Computerworld confirmed the solicitation on multiple systems.
The latest please-come-back bid followed lower-key efforts earlier this year by Google. In January, Google asked Firefox users if they wanted to reset their home page or change their default search engine to Google. Those appeals appeared in small banners atop the google.com page, not within the search results.
Since Mozilla -- Firefox's maker -- struck a deal last year that made Yahoo the default search engine for most U.S. users, Google's share has slipped by several percentage points. Google had long been Firefox's default.
According to Irish analytics vendor StatCounter and U.S.-based comScore, Yahoo gained U.S. search share during each of the first two months after Mozilla changed the default on Dec. 1, 2014.
But Yahoo's growth at Google's expense may have peaked. Two weeks ago, StatCounter noted that Yahoo's overall U.S. share had dropped to 10.7 percent from 10.9 percent in January, while Google's share had climbed one-tenth of a percentage point to 74.9 percent.
StatCounter also tracked a downturn in Yahoo searches from within Firefox. In February, U.S. Yahoo-on-Firefox usage was 27.3 percent, down from 28.3 percent the month prior. Meanwhile, Google-on-Firefox usage was 65.1 percent, up from 63.9 percent in January.
Before the Mozilla-Yahoo deal, U.S. Yahoo-on-Firefox usage was just 9.9 percent, while Google-on-Firefox usage stood at 81.9 percent.