much vs. a lot of

[Uthman]

Hi all!
Which sentence is correct and why?
I don't have a lot of time ...
I don't have much time ...
Thank you very much!

[Rusty]

Hi all!
Which sentence is correct and why?
I don't have a lot of time ...
I don't have much time ...
Thank you very much!
Both are fine.

[Uthman]

Thank you Rusty very much!
I thought "I don't have much time" is more correct because "much" is used in negative sentences.