Orange said it had sent an e-mail to staff to gauge their reaction on whether it should bid to take over the sponsorship, in time for the eighth series, starting in May.
"We're looking into whether Big Brother is an appropriate programme for us to sponsor. In fact, we've asked our 12,000 employees for their opinion," said an Orange spokesman.
"We're waiting to see what comes back from them and then we'll make a decision."
Channel 4 claimed it was in talks with "a number of high-profile brands", with speculation also surrounding Phones4U, Lynx and Toyota.
The Carphone Warehouse dropped out last week, having pulled its backing of the Celebrity Big Brother show in January over the alleged bullying of Bollywood star Shilpa Shetty by housemates including Jade Goody and Danielle Lloyd, although it said it would continue to invest "a large proportion" of its £5.5m media spend with C4, including airtime and online advertising within Big Brother programming.
Despite an ongoing investigation by Ofcom into the racism allegations, C4 claims advertisers are queuing up to back the series, which head of sponsorship David Charlesworth said remained the "daddy of the reality TV genre".