This possibility is so implausible...
The early 1500s for a Muslim reconquista are implausible, however the later 1500s provide a good POD and circumstances. Powerful United Moroccan state, growing disatsifaction of Moriscos, wars of religion within Christendom, Ottoman - Habsburg rivalry.
A PoD within the Morisco Revolt could lead to a modest Muslim state present within Iberia.
No, this possibility is so implausible that is coming to an absolute impossibility.
First... except the unlikely concerning to Morocco, the other factors were present in OTL and despite them,in OTL, this course of events did not happen and instead the opposite happened until the battle of Lepanto, marked the end of the maritime threat ottoman in the Western Mediterranean.
Then it would happen the final conquest of Granada and from then on there was no organized military threat against the Spanish Mediterranean coast.
Since the defeat of the Merinides in the Battle of Salado and Castilian control of the Strait and its main defensive enclaves: Gibraltar, Algeciras and Tarifa, which precluded any attempt at landing and African invasion, besides that should be able to defeat the Spanish fleet in the Mediterranean.
Besides, as part of this offensive should be first of its forces Islamic forces one concerted effort to conquer all the Spanish strongholds on the Mediterranean coast of Africa.
Regarding hypothetical Ottoman support is unfeasible and impossible .. we just consider the military and logistical effort involved in their failed attempts to conquer Malta.
First of all the Ottomans should conquered Malta and after this conquest should attack the Spanish possessions in Sicily and Naples, to secure their conquest. Only the conquest of Malta would require an even greater effort than the one carried out in OTL; from these numbers it is possible to project that required an attempt to conquer Sicily, which would require first isolate and then a long ground campaign, was out of the Ottoman possibilities let alone the economic, military and logistical efforts to even consider sending a fleet to fight in Spanish waters to support a hypothetical invasion force against Spain...
If not was eliminate the threat of Malta and the Spanish bases in southern Italy.
Not to mention that Spain would not remain passively waiting for his enemies and the actions of these would have the primary effect of predictable alarm and intensification of military preparations and offensive and defensive actions of Spain in response to the renewed Ottoman offensive and / or African offensive.
Assuming, of course that a hypothetical coalition of African tribes, the successor to the Merinides, achieve unity of action and have enough military power to unify Morocco and / or Algeria ... to build and equip an army and a navy European-style... and if you can do then is faced with the task of destroying the Spanish Mediterranean fleet...
Achieving this should besiege and conquer defensive enclaves mentioned above: Gibraltar, Algeciras and Tarifa; of course only from a 'voluntarist' perspective one can assume that it may happen that combination of socio-political factors and improbable military actions in favor of the Muslims.
But assuming it arrives to this favorable situation and be besieging these strongholds in Spain ... should take them before the Atlantic fleet of Spain can meet and on their way to face the rest of the Muslim fleet had defeated his countrymen of the Mediterranean fleet.
These invaders by land should confront the permanent troops then leading military power in Europe besides military troops recruited in Spain to face the threat of invasion.
These troops were the basis of the best infantry in Europe for more than a century, they would be fighting in his homeland and against which they considered their natural enemy.
Spain in the sixteenth century, there were regular army units ready always in a state of 'war footing', although there were no imminent threat.
Besides that for internal security and as a quick reaction force, in modern terms, it was created 'The Holy Brotherhood' by the Catholic Monarchs in 1476 to ensure security and maintain law and order in all the territories of the Crown, by so, it was the first national police force in the West. It was conceived as a body of permanent army of professional soldiers and militiamen.
Not counting in the number of forces available to the Spanish monarch, the mercenaries so often used by the Habsburgs and the Portuguese factor, either as an independent kingdom or united as a member of the Habsburg Monarchy; not remain indifferent to the threat posed by this alleged and hypothetical North African power and in the case discussed here, their national and religious interests undoubtedly be aligned with the Spaniards.