Verizon Communications Inc. and others are expected to bid around $2 billion to $3 billion in the auction for Yahoo Inc.’s core business, less than what the troubled Internet pioneer was expected to fetch, according to people familiar with the matter.

The telecom giant is considered the front-runner in a field that includes private-equity buyers, some of whom are expected to bid in the low end of that range, the people said. As recently as April, people close to the process said Yahoo’s core business would likely go for between $4 billion and $8 billion.

Some offers could still be above the $2 billion-to-$3 billion range, other people said, and it is generally in the interest of bidders to play down their enthusiasm in an auction. It is also possible that not everyone will bid for all of the core business and that proposals will be structured differently.

Yahoo has set a deadline in the first week of June for the next round of bids, some of the people said. It isn’t clear whether that will be the final round or if another one will follow, they said.

Bidders have lowered their expected prices following weeks of sale presentations by Yahoo Chief Executive Marissa Mayer at the company’s Sunnyvale, Calif., headquarters and its disclosure of data that detailed the company’s flagging prospects.