All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
First of all, you should know, dear sister, that it is forbidden for a Muslim woman to establish a friendly relationship with a non-Mahram man even if he is a Muslim, let alone if he is not a Muslim as we clarified in Fatwa 81356.
Therefore, if you have a friendly relationship with this non-Muslim, you are obliged to immediately cut it and repent to Allaah.
If you are in contact with him for the sake of Da’wah, then it is a man who should call him to Islam as he is more capable of calling him to Islam than a woman and you will be far from the steps of the devil who may drug you to unpleasant consequences, especially that you are attached to him and he is attached to you; so you should fear Allaah.
As regards why he is not yet guided, then guidance is in the Hands of Allaah; He guides whomever He wishes out of His Generosity, and He misguides whomever He wishes out of His Justice. When Allaah knows that someone is ready to accept guidance and that there is good in him, He guides him, as Allaah Says (what means): {Had Allaah known any good in them, He would have made them hear.}[Quran 8:23] As-Sa’di, [who is one of the interpreters of the Quran] said: “This is evidence that Allaah does not prevent faith and good except from the one in whom there is no good and who is not virtuous (in His Sight) and who would not respond [i.e. who would not accept guidance].”
Indeed, you find some people even if they see in front of him the unshakable mountains fight each other, and see great sings and evidence come to him, he would persist on disbelief because his heart is blind and because of his stubbornness. Indeed, Allaah Says about such people (what means): {And even if We had sent down to them the angels [with the message] and the dead spoke to them [of it] and We gathered together every [created] thing in front of them, they would not believe unless Allaah should will. But most of them, [of that], are ignorant.}[Quran 6:111] Allaah also Says (what means): {… and if they should see every sign, they will not believe in it.}[Quran 7:146]; it means no matter how much of the signs, evidence, proofs they see, they would not believe in them; Allaah Says as well (what means): {And [even] if We opened to them a gate from the heaven and they continued therein to ascend. They would say, “Our eyes have only been dazzled. Rather, we are a people affected by magic.”}[Quran 15:14-15]
Therefore, it might be that the polytheist to whom you are attached is of this kind; we seek refuge in Allaah from this.
Hence, you should fear Allaah and not be attached to him as there are many Muslims who are better than him in religion, moral conduct and beauty. You should remember the Saying of Allaah (which means): {And do not marry polytheistic men [to your women] until they believe. And a believing slave is better than a polytheist, even though he might please you. Those invite [you] to the Fire, but Allaah invites to Paradise and to forgiveness, by His permission.}[Quran 221]
However, it is permissible for a male relative of yours or any other man to call him to Islam as we previously mentioned but you should be careful and not hasten to marry him if he announces his becoming a Muslim, as he might do so for the purpose of marrying you and not due to having a desire to be a Muslim.
For more benefit on the prohibition of a Muslim woman's marriage to a non-Muslim man, please refer to Fatwa 84265, and to Fataawa 21363 and 84345 on how to call non-Muslims to Islam especially Hindus, and to Fataawa 81979, 86091 and 88906 on an introduction to Islam and that Islam is the true religion.
Allaah Knows best.