Both forms are correct. When we consider check and cheque as nouns, they are both different forms of the same word. In that case, check is the American English version, and cheque is used in British English. What is interesting, the spelling cheque is used only since the early XIX century and only in a financial context. On the other hand, check as a verb cannot be replaced by cheque. There are also a few different meanings of check being nouns that are correct only in this version of spelling.

Correct spelling, explanation: form is used in American English (as a noun) and British English (as a verb).

Correct spelling, explanation: form is used in British English (only as a noun).

Definition of check/cheque:
noun: a printed form that can be used to make payments instead of money;
I do not have enough cash, can I pay by cheque?
I remember my grandfather always paying by check in restaurants.

Definition of check:
verb: to examine something or someone if it is correct or safe;
I always check my answers twice before I finish an exam.
– to verify something;
I have to call the garage and check if my car is ready to pick up.
– to leave a thing, ex. luggage or a piece of clothing, to someone to have them take care of it for some time;
Do not forget that we need to check (out) our luggage as soon as we get to the airport.
I will just check my coat and we can meet at the bar.
– to mark something as complete;
I love to check items off my to-do lists.
noun: a pattern of squares composed of lines in different colors crossing each other;
My favorite suit has a gray check pattern.
– a mark that shows a complete task (✓ );
Put a check on the correct box representing your sex.