Which one is correct: to have a small chat/talk or to have a short chat/talk?
A little chat.
But I'm American--I'd be interested to see if it changes by region.
A 'short chat' is possible, as is a 'little chat/talk'. The latter is more informal, in my opinion.
A 'short talk' is likely to be a short lecture, and 'small talk' is polite conversation about unimportant things.
A small talk (with you)... This may be AmE only.
A short chat with you...
A little word with you...
Small talk is also a noun: polite conversation about unimportant or uncontroversial matters, esp. as engaged in on social occasions : propriety required that he face these people and make small talk.
John