(UPDATE: Verizon is denying the Reuters report, although as Re/code points out, the company "also denied it was buying AOL months before it did just that.")

Verizon is thinking about selling off its Terremark data center and cloud business, Reuters reported on Friday, citing unnamed sources.

If true, it would be another sign that companies are ceding the cloud services market — public cloud, in particular — to the biggest of the big. It would follow HP's announcement (before splitting into two businesses) that it would stop offering public cloud services.

In a similar move, CenturyLink announced this week that it's exploring options for selling data centers. That decision appears to be more related to the colocation business than to cloud services.

These companies aren't exactly minnows. But the public cloud is overwhelmingly dominated by Amazon Web Services (AWS), which happens to also be racking up profits. Some analysts believe cloud services will be a game for a handful of players, with AWS, Microsoft Azure, Google Cloud, and IBM Softlayer among the contenders.

Not every player is dropping out. VMware has doubled down on the cloud, turning Virtustream (acquired by VMware parent EMC for $1.2 billion) into the latest member of the EMC Federation. And Oracle showed at the recent OpenWorld conference that it's obsessed with the cloud and is willing to charge AWS head-on.

For Verizon, a Terremark sale would be part of a larger divestment of enterprise services, Reuters reported. That would include MCI — remember MCI? — which still has enterprise customers who pay for broadband and, yes, landline services.

Verizon paid $1.4 billion for Terremark in 2011. Reuters' sources estimate that Verizon's enterprise assets could command a price of $10 billion.