Here are Melbourne hotels that advertise a 24‑hour business centre (or business centre listed as 24/7). I’ve linked the source(s so you can confirm details and current hours with the hotel directly.

• Sofitel Melbourne On Collins — luxury hotel on Collins Street; lists a 24‑hour business centre. (sofitel-melbourne.com.au)
• Novotel Melbourne on Collins — central CBD hotel (Collins St) with a 24‑hour business centre listed on hotel pages. (novotelmelbourne.com.au)
• Pullman Melbourne on the Park — near Fitzroy Gardens/MCG; property listings show a 24‑hour business centre. (pullmanonthepark.com.au)
• Pullman (Pullman Melbourne City Centre / on Swanston) — city‑centre Pullman property lists business services and is shown as 24‑hour in several hotel listings. (all.accor.com)
• PARKROYAL Melbourne Airport (Pan Pacific Group) — airport hotel that explicitly lists its business centre as open 24/7. (panpacific.com)

Quick notes

• Hotel websites and third‑party booking pages sometimes disagree or don’t publish exact hours for business centres; I recommend calling the hotel front desk to confirm 24/7 access (and whether services like printing/scanning are staffed overnight).
• If you want I can: (a) check specific hotels’ current business‑centre hours and contact numbers, or (b) find 24‑hour business centres in a particular area of Melbourne (CBD, Southbank, near the airport). Which would you prefer?