The initiative is part of wide-reaching changes taking place at the broadcaster, which occupies Channel 4's terrestrial slot in Wales.
The channel is seeking agencies with experience in creating identities for TV channels and establishing them both on- and off-air.
S4C airs more than 80 hours of programming a week, including sport, music, live events, drama, news and children's shows.
The rebrand is part of a restructure at the broadcaster as it faces up to the challenge of audience segmentation driven by the rise of digital TV. A new management team has been appointed to pursue the strategy.
S4C, which launched in 1982, is funded by a fixed annual budget from the Treasury and advertising revenue.