sajangnimi da-eum dare gyeyak naeyongeul dasi hwaginhajago haesseo.

The boss said we should check the contract details again next month.

Breakdown of sajangnimi da-eum dare gyeyak naeyongeul dasi hwaginhajago haesseo.

• ~이: subject particle
• ~을: object particle
• 다음: next
• ~에: time particle

Questions & Answers about sajangnimi da-eum dare gyeyak naeyongeul dasi hwaginhajago haesseo.

What does -자고 했어 mean in this sentence?

-자고 했어 is the indirect-quotation form for a suggestion.

• 확인하자 = let's check / let's confirm
• 확인하자고 했어 = (someone) said we should check / suggested checking

So the boss is not simply stating a fact. He is proposing that they check the contract details again next month.

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How is 확인하자고 했어 different from 확인하라고 했어?

They are similar, but the nuance is different:

• 확인하자고 했어 = said, “let’s confirm/check”
  → a suggestion including the speaker/listener group
  → like Let’s check it again

• 확인하라고 했어 = told (someone) to confirm/check
  → more like an instruction or command
  → like He told us to check it again

So in your sentence, the boss is presented as suggesting a joint action, not just ordering someone else to do it.

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Why is it 사장님이 and not 사장님은?