Is there a version of Parallels for MacOS that will virtualize Mac OS X 10.4.1 in a VM?

Looks like nothing older than Leopard Server (10.5). But I suppose you could try.

For the record, here is the complete list:

Guest Operating Systems

  • Windows 10
  • Windows 8.1
  • Windows 8
  • Windows Server 2019
  • Windows Server 2016
  • Windows Server 2012 R2
  • Windows 7 (SP0-SP1)
  • Windows Server 2008 R2 (SP0-SP2)
  • Windows Vista Home, Business, Ultimate, Enterprise (SP0-SP2)
  • Windows Server 2003 R2 (SP0-SP2)
  • Windows XP (SP0-SP3)
  • Windows 2000 Professional SP4
  • Windows 2000 Server SP4
  • MS-DOS 6.22 **
  • Boot2Docker
  • Red Hat Enterprise Linux (RHEL) 7, 6, 5
  • CentOS Linux 7, 6, 5
  • Fedora Linux 28, 27, 26
  • Ubuntu 18.10, 18.04 LTS, 17.10, 16.04 LTS, 14.04 LTS, 12.04 LTS
  • Debian GNU/Linux 9.4, 9, 8, 7
  • Suse Linux Enterprise 15, 12 SP3, 11 SP3, 11 SP2
  • OpenSUSE Linux 15, 42.3, 13.2, 13.1, 12.3
  • Linux Mint 19, 18, 17
  • Kali 2018.2, 2018.1, 2
  • Elementary 5.0, 0.4
  • Manjaro 17
  • Mageia 6, 5, 4, 3
  • Gentoo Linux **
  • Solaris 11.3, 11, 10 **
  • openBSD 6 **
  • FreeBSD 11.1, 10, 10, 9, 8 **
  • openVZ 7
  • eComStation 2, 1.2 **
  • ReactOS 0.4 **
  • Android OS*
  • macOS Mojave 10.14.x
  • macOS High Sierra 10.13.x
  • macOS Sierra 10.12.x
  • OS X El Capitan 10.11.x
  • OS X Yosemite 10.10.x
  • OS X Mavericks 10.9.x
  • OS X Mountain Lion 10.8.x
  • OS X Lion 10.7.x
  • OS X Lion Server 10.7.x
  • Mac OS X Snow Leopard Server 10.6.x
  • Mac OS X Leopard Server 10.5.x
  • * — Only the one downloaded with help of Installation Assistant.
    ** — Parallels tools are not available for this operating system.