Core Rules
No
From the spell description p. 283
If you turn a creature into another kind of creature, the new form can be any kind you choose whose challenge rating is equal to or less than the target’s (or its level, if the target doesn’t have a challenge rating)
It explicitly states that creatures without challenge ratings have levels. This implies that creatures with levels do not have challenge ratings.
The spell only allows you to turn the target into a creature with a challenge rating - not a creature with levels.
For example, you can choose any of the humans in the monster manual, the priest, the assassin, the archmage etc. but you cannot choose a Human Wizard Level 19 because this creature has no challenge rating.
Optional Rules
Yes, but its not straightforward.
From p. 283 of the DMG for NPCs and Monsters with Classes respectively:
... then determine the NPC's challenge rating just as you would
for a monster.
You'll need to recalculate its challenge rating as though you had
designed the monster from scratch.
The older edition paradigm of CR=Level does not hold true in 5e.
It would take some considerable time to determine the CR of you Kobold + Wizard level monster and is likely to bog the game down dramatically if it happens during a session. If this is something that you want, I suggest the DM and the wizard decide on a few "go to" polymorphs and work them out in advance.
This appears to be how the Monster Manual Appendix B NPCs were assigned their CR.