I should have looked up the exact wording before writing instead of relying upon rules memoy.
It does have language about your existing class minimum. I was only remembering the new class language. And the narrative emphasis fluff about requiring being a quick study in the new class. "Without the full training that a beginning character receives, you must be a quick study in your new class."
MULTICLASSING
Multiclassing allows you to gain levels in multiple
classes. Doing so lets you mix the abilities of those
classes to realize a character concept that might not be
reflected in one of the standard class options.
With this rule, you have the option of gaining a level
in a new class whenever you advance in level, instead
of gaining a level in your current class. Your levels in
all your classes are added together to determine your
character level. For example, if you have three levels in
wizard and two in fighter, you're a 5th-level character.
As you advance in levels, you might primarily remain
a member of your original class with just a few levels
in another class, or you might change course entirely,
never looking back at the class you left behind. You
might even start progressing in a third or fourth class.
Compared to a single-class character of the same level,
you'll sacrifice some focus in exchange for versatility.
PREREQUISITES
To qualify for a new class, you must meet the ability score
prerequisites for both your current class and your new
one, as shown in the Multiclassing Prerequisites table.
For example, a barbarian who decides to multiclass into
the druid class must have both Strength and Wisdom
scores of 13 or higher. Without the full training that
a beginning character receives, you must be a quick
study in your new class, having a natural aptitude that
is reflected by higher-than-average ability scores.
MULTICLASSING PREREQUISITES
Class Ability Score Minimum
Barbarian Strength 13
Bard Charisma 13
Cleric Wisdom 13
Druid Wisdom 13
Fighter Strength 13 or Dexterity 13
Monk Dexterity 1 3 and Wisdom 13
Paladin Strength 13 and Charisma 13
Ranger Dexterity 13 and Wisdom 13
Rogue Dexterity 13
Sorcerer Charisma 13
Warlock Charisma 13
Wizard Intelligence 13
So current class is a bit ambiguous but sounds to me like the one you took for your most recent level. If they had meant your original class I think they would have said so.
If your last/current class is rogue you can multiclass to monk by my reading RAW because you have the rogue and monk class prereqs.
By the same account if your last level was wizard and you can no longer multiclass out of it, the question of whether you can take a level of rogue is interesting. I would not read rogue in these circumstances as a new class.
It is possible to read current class as all your current classes in which case you can't multiclass into a new one now that you have lost the wizard prereq.
A ruling not rules situation to check with how your DM wants to handle it.
I think current class means all the classes you currently have. Also if "current class" is just the last class you took then if my last class was Wizard I could not take a Monk level but I could also not take any more Rogue levels as Wizard is my "current class" so I would only be able to take more Wizard levels.