
The Brit Award winner, 32, has been romancing Lowe since he was introduced to her by Sean Lennon earlier this year, according to The Sun.
He took the Agent Provocateur worker to the Brits as his secret date and allegedly flew her out to Miami for a holiday.
Ronson, who recently split up with his long-term US girlfriend, artist Cosi Theodoli-Braschi, has been spending time with her at his homes in Oxfordshire and New York.
"Mark has put everything into romancing Daisy," said a source. "She is a stunning girl and he was dead set on making her his new girlfriend.
"He has pulled out all the stops to impress her. She is living between London and New York, as does Mark, so there is no problem with long-distance relationship headaches."
Lowe's parents are former indie star Pearl Lowe and Gwen Stefani's husband Gavin Rossdale.
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