The so-called “trolls” mocked 23-month-old Riley Hoult, from Leeds. who is being treated for childhood cancer neuroblastoma.
Riley’s mother Sophie Hoult, 20, of Middleton, set up Twitter accounts in Riley’s name on Facebook and Twitter to share her son’s cancer fight story in a bid to raise awareness of neuroblastoma.
She was disgusted last month when another Twitter account - @funny_cancer - was set up using a photograph of Riley before posting tweets including ‘cancer is funny because people die.’
Miss Hoult later received upsetting tweets mocking her son’s appearance from another Twitter account.
Both accounts were closed down by Twitter.
Det Chf Insp Lisa Atkinson, head of Leeds CID, said: “We have been carrying out extensive enquiries to identify the people responsible for making offensive postings on social media in relation to 23-month-old Riley Hoult from Leeds who is receiving treatment for cancer.
“We have been to see Riley’s mother to take a formal statement and to reassure her that we will do everything we can to take action against those responsible.
“We are now in dialogue with Twitter to see how to see this matter can be progressed.
“We have previously taken action against people who have made offensive comments on social media which resulted in them being given prison sentences.”
Twitter chief executive Dick Costolo recently promised to do more to tackle those who hurl abuse on its service, admitting the company was losing users as a result.