The couple, who announced their separation in February, will have their case heard in the High Court at 10am, according to The Sun.
The case has apparently been listed as 'CAC v AC' - in reference to the pair's initials - and tops a list of 29 other divorces due for today.
Neither star is expected to attend the procedure, in which a judge is expected to grant Cheryl a decree nisi that ends the couple's four-year marriage.
A source said: "Cheryl is in the States but is watching things very closely. She is relieved and pleased things have progressed significantly since her illness.
"She just wants to move on with her life and getting the divorce done will end a very painful chapter."
They added: "It must not be forgotten Cheryl did not ask for this. The last thing she expected was to be a divorcee at 27.
"But once she accepted there was no way the marriage could work without the trust destroyed by her husband, the pill was a slightly less bitter one to swallow.
"She and Ashley have no need to stay in touch and all housing and assets will be handled by their legal representatives."
Cheryl is said to have filed for divorce in May on the grounds of unreasonable behaviour, but proceedings were held up when the singer contracted malaria in July.
It was reported last month that Cheryl believes finalising her divorce from Ashley to be "the final major obstacle to her recovery".