Published Monday, 12 July 2010
The 27-year-old X Factor judge contracted the disease on a trip to Tanzania last month, despite taking tablets to protect against the disease.
She is now recovering at a private clinic after leaving intensive care.
Speaking last night at the launch of a charity to help burns victims, Cowell said: "I had a text from her yesterday".
"She is on the mend and looking forward to coming back to work".
"She is making a good recovery."
Cole had to pull out of the final auditions and judging the boot camp stage of the forthcoming series of the talent show because of the illness. She has also had to pull out of a performance at next month's V Festival.
Cowell said he wanted to make sure she did not return to the series too early and risk becoming ill again.
Cole was reported to have collapsed during a photo shoot for her album on July 3 and was initially diagnosed with exhaustion.
She was rushed to hospital the next day after her symptoms, including a soaring fever, worsened.
The singer was treated in intensive care at University College London Hospital, home to the Hospital for Tropical Diseases, but on Friday was considered well enough to be transferred to a private clinic to continue her recovery.
Cole spent six days in Tanzania, on Africa's east coast, with close friend Derek Hough following her split from England footballer Ashley.
Malaria is caused by the parasite plasmodium, which is transmitted by the bites of infected mosquitos.
If not treated promptly, it can become life-threatening by disrupting the blood supply to vital organs.
Nine people die on average in the UK each year from malaria. Around 850,000 die annually around the world, mostly pregnant women and children under five in Africa.