According to The Guardian, the rebrand will see 1Xtra adopt two new straplines - "Xtra RnB" and "Xtra Hip Hop" - to better indicate it as Radio 1's urban music spin-off. The station will also get a new logo blending the two station's branding.
The rebranding of 1Xtra is part of the BBC's new strategy for its radio stations, including the controversial planned closure of 6 Music and the Asian Network.
Under the new strategy, the corporation wants to create and support a series of brand extensions for its five main radio networks - Radio 1, Radio 2, Radio 3, Radio 4 and Radio 5 Live.
To complement Radio 1Xtra and Radio 5 Live Sports Extra, Thompson wants to rebrand Radio 7 as Radio 4 Extra. Senior BBC sources also suggest that 6 Music could become Radio 2 Extra to placate strong opposition to its closure.
Over the next 18 months, the BBC Executive will more closely tie 1Xtra's editorial schedule to parent station Radio 1 and grow its modest audience to a "sustainable scale".
1Xtra currently has a relatively low weekly reach, which has led to calls for it to be shut instead of 6 Music. Tim Westwood, the station's most high-profile DJ, recently complained that he had been broadcasting "to absolutely nobody for the last three hours - it's soul-destroying".
The BBC said that 1Xtra's new "Xtra RnB" and "Xtra Hip Hop" straplines will help create a "front door" for the station's wider musical playlist, which includes dancehall, dubstep and house music.
A BBC spokeswoman said: "These two genres should act as the front door into the rest of the station, giving the audience a clear message about the core offering and a route in, where we can then inform them of the range of music 1Xtra has to offer."