AOL (AOL) and Yahoo! (YHOO) are having little luck competing on their own in todays tech world, but there are new signs that at least one side would like them to consider joining forces.

According to Bloomberg News, AOL CEO Tim Armstrong is discussing a potential combination in the wake of Yahoo!s dismissal of CEO Carol Bartz earlier this week. Yahoo! had already reportedly been in talks with its financial advisers over its strategic options.

Any combination would presumably consist of Yahoo!, which has a market cap of $18.2 billion, absorbing AOL, which is worth just $1.6 billion.

The two struggling companies, which increasingly appear to be dinosaurs of the old tech world, have talked about a merger before in an effort to fend off competition from Google (GOOG) and Facebook.

While Yahoo! shot down New York-based AOLs overtures last year, Bartzs ouster led Armstrong to approach private equity firms and investment bankers from Allen & Co. that are representing Yahoo!, Bloomberg reported.

However, Sunnyvale, Calif.-based Yahoo! is unlikely to have an appetite to scoop up AOL due to the companys heavy losses and slumping revenue, the wire service reported.

During her brief tenure, Bartz struggled to turn things around at Yahoo!, which rebuffed a $47.5 billion buyout bid from Microsoft (MSFT) in 2008.

Meanwhile, AOL, which was spun off from media giant Time Warner (TWX) two years ago, continues to face challenges even after acquiring The Huffington Post earlier this year for $315 million.

Shares of AOL declined 2.83% to $15.10 Friday afternoon, while Yahoo! dipped 1.32% to $14.26.

Follow Matt Egan on Twitter @MattMEgan5