Is it permissible for him to accept zakaah when he has property that is rented out?

It is permissible to give zakaah to one who does not have
enough for his maintenance, even if he has property that he rents out,
because this is a case of one who is needy (miskeen) and is mentioned in
the verse in which Allah says (interpretation of the meaning):
“As-Sadaqaat (here it means Zakaah) are only for the Fuqaraa’ (poor), and
Al‑Masaakeen (the poor)…” [al-Tawbah 9:60]. Al-Nawawi (may Allah have
mercy on him) said: The miskeen (poor, needy) is the one who is able to
acquire money or income to meet some of his needs but it is not enough for
him. End quote from al-Minhaaj ma‘a Sharhihi Mughni al-Muhtaaj,
4/176. 

And Allah tells us in the story of Moosa (peace be upon him)
with al-Khidr about the poor and needy people who owned a ship. Allah says
(interpretation of the meaning):

“As for the ship, it belonged to Masaakeen (poor people)
working in the sea…”

[al-Kahf 18:79].

They did not cease to be regarded as miskeen even though they
owned a ship.

 Based on that, if he has accommodation that he rents out,
but what he gets from it is not sufficient for him, it is permissible to
give zakaah to him, because he is included in the verse which describes the
categories of people to whom zakaah may be given. 

Imam Maalik (may Allah have mercy on him) said: If a person
has a house and servant and nothing else, he may be given zakaah. 

End quote from al-Mudawwanah, 3/221 

Al-Nawawi (may Allah have mercy on him) said: If he has
property but the income from it is less than is sufficient for him, then he
is faqeer or miskeen [poor or needy] so he may be given zakaah to ensure he
has sufficient to live on, and he should not be made to sell his property.

End quote from Sharh al-Muhadhdhab, 6/174 

In Kashshaaf al-Qinaa‘ (2/273) it says: Imam Ahmad
said according to the report of Muhammad ibn al-Hakam: If he has a farm or
property that he rents for ten thousand or more, but it is not enough for
him, he may receive zakaah. … End quote. 

To sum up: If a person has property that he rents out, but
what he gets from it is not sufficient for him, it is permissible to give
him zakaah to make up what he has, so that it will be sufficient for him and
for those on whom he spends, such as his children, wife, father and mother. 

And Allah knows best.