AOL Inc. and several private-equity firms are exploring making an offer to buy Yahoo Inc., according to people familiar with the matter, devising a bold plan to marry two big Internet brands facing steep challenges.

Silver Lake Partners and Blackstone Group LP are among the firms that have expressed interest in teaming up with AOL to buy Yahoo or trying to take it private on their own, these people said. They added that at least two or three other firms could be interested in participating if a formal buyout...