A Google job advertisement indicates it may be planning to build a telephone customer support operation for Nexus One users. The news comes after the company received complaints over its web-only support.

The Digital Inspiration blog noticed a Google job advertisement for a phone support program manager for Android and the Nexus One.

The position includes building and managing telephone support for Android and Nexus One customers, according to the job posting. It is not clear if Google will be handling the operation entirely internally or if it will partner with an outsourced call-center operation.

Google spokeswoman Katie Watson declined to answer questions about the company’s plans.

Shortly after the Nexus One was released, Google faced a deluge of complaints from users struggling to find help for various problems. Many contacted T-Mobile only to be referred to HTC, which often directed customers back to T-Mobile. Google accepts only email queries, in addition to its online help forum, to which it responds in one or two days.

While it appears that Google was unprepared initially to support phone customers, it has begun to be more responsive on the help forums. On Tuesday it pushed out a Nexus One software update to fix a problem that some people had with connecting to 3G networks.