MSC offers shuttle service between Genoa and Linate or Malpensa airport, both ways.
We have used it several times.
Today i have booked Genoa to Linate 4/12 2023 for € 39 p.P.
Old PDF (from 2016) with more information(sorry, only in german):
https://msc.mykreuzfahrt.de/anreise-abreise-transfer.pdf
I found a newer one:
https://www.msccruises.de/-/media/germany/documents/deu_flughafen.pdf