rephrase

This word carries a negative meaning.
This word connotes a negative meaning.

This word bears a negative meaning.
This word has a negative meaning.

These seem fine; the second is more common, certainly; no others spring to mind. If you supply a particular word, something else, like 'connotation', may be more appropriate.

Thank you both.

'Connoting a meaning' sounds odd to me; it is off-balance in some way. 'Connote an additional meaning' would work.

Mister Micawber'Connoting a meaning' sounds odd to me; it is off-balance in some way. 'Connote an additional meaning' would work.

I agree but people say it sometimes so it's not exactly wrong. Anyway, it's "connote a negative meaning", not just "connote a meaning".

Ivanhrso it's not exactly wrong.

Right.

Thanks, and just for conclusion:

This word carries a negative meaning.
This word connotes a negative meaning.
This word bears a negative meaning.
This word has a negative meaning.

One more question! Do you think connote can be used to talk about ironic meanings? e.g. to ask if a sentence has or hasn't an irony in it. I tried to think up an example, but it is just occurred to me so I am not sure if I could give you a good example.

This word connotes a negative meaning.-- No, I'm still not happy with this one as a natural utterance. I can find no examples on COCA, and Google calls up very few.

Do you think connote can be used to talk about ironic meanings? e.g. to ask if a sentence has or hasn't an irony in it.-- Yes, indeed; irony can be one kind of connotation.

Ivanhr Mister Micawber'Connoting a meaning' sounds odd to me; it is off-balance in some way. 'Connote an additional meaning' would work.I agree but people say it sometimes so it's not exactly wrong. Anyway, it's "connote a negative meaning", not just "connote a meaning".

No. A word can't "connote a meaning", negative or otherwise. It connotes a concept. That p