One needs to take ablution to perform tawaf, otherwise the tawaf is invalid. This is because Tawaf is similar to a prayer, based on a hadith narrated by Ibn Abbas :

"الطواف صلاة إلا أن الله تعالى أباح فيه الكلام"

Which means: "Tawaf is a prayer, except that you may speak during it (tawaf)". (Narrated by Ibn Hibban and Hakim)

So if one forgets yet he is convinced that he is in the state of ablution while doing tawaf then he may follow what he is certain of. This is based on the Fiqh method :

"اليقين لا يزال بالشك"

Which means: "Certainty is not overruled by doubt"

If while performing tawaf he then recalls that he was not in a state of wudhu, then it is obligatory for him to take the wudhu and renew his tawaf.