Can malware be transferred to external hard drive

Hello,

I'm planning on buying a new computer as my current one seems to have viruses and Malware I can't get rid of. I don't want to restore my new machine from a time machine backup as I don't want the Malware to potentially get on the new computer. So I plan to manually transfer the important folders and documents via an external hard drive.

Is there a possibility that the viruses or Malware can be transferred on to the external and then over to the new computer? If this is the case, how is it possible to transfer files without having to upload them to the internet via Google Drive or Dropbox? What's the safest way to do so without transferring malicious programs to your computer?