Offer Specifics, Not Availability

"Let me know if I can help" → "I can draft the first version of the Q3 report by Wednesday if that helps."

Vague availability gets thanked and forgotten. Specific offers get accepted, because the other person does not have to figure out how you could help.

Three tests for a strong offer: a named task, a named timeframe, and a check-in the other person can simply say yes or no to. All three fit in one sentence.