In an interview with The Independent, the director confirmed that it was already working on a third part with Alex Garland, the original "28 days later" screenwriter:
"We have an excellent idea with Alex with Alex. Truly good. "
Boyl details, of course, share to refuse, but mentioned that it would be something completely "fresh", and the action in the film is likely to unfold "28 months later" of the original events. What can be a "fresh look" on the zombie drama genre, you may find out soon enough - while Danny Boyle does not mean any new projects, so the director is full of time to work on the tricvel.
Excerpt from the original:
The horror film "28 days later" by the efforts of Danny Boyla saw the light in 2002; Horror, the main role in which Killian Murphy played brilliantly, unexpectedly became a hiring hit and earned 10 times the budget (80 million dollars). 5 years later, Sikvel came out, to which Danny Boyle did not have a relationship - "28 weeks later" gathered such stars in the caste, like Jeremy Renner, Idris Elba and Rose Byrne, but the original did not manage to surpass, collecting 65 million dollars.