"I can confirm that we are following the call for bids with interest and see ourselves as potential participants," PWC spokesperson Eva Oberholzer told Swiss weekly NZZ am Sonntag.
Of the potential partnership with the Red Cross, she said: "We are convinced that our core competencies will complement each other."
In the coming months, Swiss migration authorities are set to announce which services will be outsourced as part of sweeping changes to the country's asylum system. Those contracts are expected to worth a total in the hundreds of millions.
Among the reforms is access to free legal advice for asylum seekers, and it is this service that PWC has now said it may bid for.
The contract is thought to be worth 25–35 million francs a year.
The new reforms to the Swiss asylum system are designed to speed up the asylum process by guaranteeing faster deportation for people whose applications are rejected and more rapid integration into the job market for those given permission to stay.
To carry out these tasks the Swiss government has spent around 550 to 600 million francs on building and renovating 20 dedicated reception and processing centres.
Annual running costs are expected to be 150 to 200 million francs with many services going to external suppliers.