Private-equity firms KKR & Co. and Silver Lake Partners, along with a third investor, are nearing a deal to buy GoDaddy Group Inc., a closely-held company that registers Internet domain names, for between $2 billion and $2.5 billion, people familiar with the matter said.

An announcement of the sale could come as early as next week, although a deal hasn't been signed yet and the people cautioned that an agreement may not be reached.

Private...