Time machine doesn't see my network drive
I have an old MacbookPro from 2012 and I could get Time Machine to work on it successfully. It currently backs up to a network drive (exFAT format) connected through my router.
I have a new MacBook Pro recently purchased. I was able to access the network drive and manually put files in there via SMB. However, the Time Machine can't see that I have a connected and working network drive. It informs that I do not have a suitable Time Machine destination. Would appreciate if anyone has a solution to this.
MacBook Pro 14″, macOS 13.1