All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
It is permissible for you to supplicate even if you are not in a state of ablution, but it is more appropriate for you to supplicate Allah while you are in a state of purity. Shaykh Ibn Baaz said:
"There is no harm in offering Du’aa' without performing Wudhoo', and even if you are in the state of Janabah (major ritual impurity related to sexual discharge). Wudhoo' is not one of the preconditions of Du’aa'. This is a mercy from Allah (Glorified be He) because a slave is always in need of Du’aa'. However, offering Du’aa' whilst in the state of Wudhoo' and during the prayer increases the likelihood of your Du’aa' being answered, especially whilst in prostration because of the Prophet's saying: 'The position during which the slave is nearest to his Lord, is when he is in prostration, so abundantly supplicate (in this position)’. [Muslim].” [End of quote]
The person may also supplicate in any situation, whether he is lying down, sitting, or standing. When interpreting the Saying of Allah (which means): {And when affliction touches man, he calls upon Us, whether lying on his side or sitting or standing; but when We remove from him his affliction, he continues [in disobedience] as if he had never called upon Us to [remove] an affliction that touched him. Thus is made pleasing to the transgressors that which they have been doing.} [Quran 12:12] Imaam Al-Qurtubi said: “Allah mentioned the three situations of supplication because a person would only be in one of these three. Some (scholars) said: ‘Allah started mentioning a person lying on his side because his affliction is harder in general, so he supplicates more and endeavors more; then the one who is sitting down, and then the one who is standing.” [End of quote]
Allah knows best.