Techniques in a wireless device for use in negotiating a group owner with another wireless device for establishing a wireless peer-to-peer (P2P) network having a connection to an external network are described. The wireless device identifies whether it is operating for communications via a home network or a non-home network. The wireless device sets its group owner intent value to an increased value when it is identified to be operating for communications via the home network, or to a decreased value when it is identified to be operating for communications via the non-home network. The wireless device then sends to the other wireless device a message which includes the group owner intent value for the wireless device. Once the group owner is selected, the wireless device will connect with the other wireless device for establishing the wireless P2P network having the connection to the external network.