Perhaps a better title might be "Is it possible for Allah to love?"
Let me first respond to criticisms Muslims may raise to the question. In the Qur'an, the word 'love' is associated with Allah a number of times. But in these verses, Allah's love is conditional. It is dependent on the actions of the one seeking Allah's love. In a sense, one must be deemed worthy of Allah's love. One must earn the right to be loved by Allah. And in this sense, the word does not mean 'love' in the way most people understand the word. The word 'respect' could easily replace 'love' and not alter the meaning of the text.
Sura 2:222 Truly, Allâh loves those who turn unto Him in repentance and loves those who purify themselves.
Sura 61:4 Verily, Allâh loves those who fight in His Cause in rows (ranks) as if they were a solid structure .
Sura 3:76 Yes, whoever fulfils his pledge and fears Allâh much; verily, then Allâh loves those who are Al-Muttaqûn [pious].
Sura 2:195 Truly, Allâh loves Al-Muhsinûn (the good-doers).
Sura 60:8 Verily, Allâh loves those who deal with equity.
Sura 9:108 And Allâh loves those who make themselves clean and pure.
Sura 3:146 And Allâh loves As-Sâbirin (the patient ones, etc.).
Sura 5:42 Verily, Allâh loves those who act justly.
Sura 3:159 Then when you have taken a decision, put your trust in Allâh, certainly, Allâh loves those who put their trust (in Him).
Sura 49:9 Verily! Allâh loves those who are equitable.
Clearly Allah does not love unconditionally like the God of the Bible.
Now, why is it impossible for Allah to love?
First, we need to understand the Islamic concept of God. Allah is tawhid, which means Allah is absolutely singular in nature. He has no parters as the Quran clearly states.
Sura 4:48 Verily, Allâh forgives not that partners should be set up with him in worship, but He forgives except that (anything else) to whom He pleases, and whoever sets up partners with Allâh in worship, he has indeed invented a tremendous sin.
Sura 3:64 Say (O Muhammad SAW): "O people of the Scripture (Jews and Christians): Come to a word that is just between us and you, that we worship none but Allâh, and that we associate no partners with Him, and that none of us shall take others as lords besides Allâh. Then, if they turn away, say: "Bear witness that we are Muslims."
Sura 5:72 Surely, they have disbelieved who say: "Allâh is the Messiah ['Iesa (Jesus)], son of Maryam (Mary)." But the Messiah ['Iesa (Jesus)] said: "O Children of Israel! Worship Allâh, my Lord and your Lord." Verily, whosoever sets up partners in worship with Allâh, then Allâh has forbidden Paradise for him, and the Fire will be his abode.
Since Allah has no partners, is absolutely singular in nature. Allah was all alone, by Himself in eternity past before the rest of creation existed. And if Allah was all alone in eternity past, on whom was he loving?
The concept of love requires at least two entities to make sense: a lover and someone or something else on whom that love is bestowed. You have to love someone; you have to love some thing. Love cannot exist in absolute, singular isolation. Thus Allah, as an absolute singular entity was unable to ever develop the attribute of love in eternity past. Allah cannot be said to possess the attribute of love.
Al-Ghazali put it this way: "Love is to sense a need of the beloved and since Allah cannot be said to have a need or an experience of need, it is therefore impossible that Allah should love." Al-Ghazali recognized that for love to make sense, another entity needed to be involved. And since Allah cannot be said to have a need of anyone or anything else to define himself, it is impossible for Allah to be said to be loving, since that requires somebody else.
But this presents a problem for Muslims, because they recognize their ability to love others. But if Allah does not possess the attribute of love and never could have in eternity past, is it logically possible Allah could have given mankind something Allah himself did not possess when he created man? Muslims claim the ability to love, but they can't claim it comes from Allah. They have the wrong God. So where does love come from?
The God of the Bible has ALWAYS existed in a loving, eternal relationship. Three persons in one shared God-head. The Father in eternal loving communion with The Son, in ever loving communion with The Spirit, in ever loving communion with The Father.
We are made in God's image (Genesis 1:26). We are loving creatures because our God has always been loving. The creator God of the Bible was able to give us the ability to love because He himself has always been loving also. He was able to give us the attribute of love because He also possessed that attribute.
Muslim are claiming an attribute they have no right to lay claim to, since they can't get it from Allah. In order for Muslims to understand who they are as loving people, they must reject Allah and come to the God of the Bible.