The 32-year-old rapper, real name Stephen Manderson, split from his wife Millie Mackintosh in February 2016 but has now moved on to Rothschild and has been on a string of dates with her, reported Female First.
The pair, who both live in London, have reportedly been "inseparable", although they have been playing down romantic chat.
"Kate and Stephen have started quietly dating. They've been inseparable the last couple of weeks. Lots of people in the Chelsea scene are talking about it," a source said.
Rothschild split from her husband Ben Goldsmith, with whom she has three children, in 2012, and is said to not want to go public with her romance with Green yet.