Is it permissible to perform Istikhara prayer for marriage to someone who has not yet proposed to me, while persistently making supplication for that?

The Istikhara prayer is performed when one is concerned about a matter or intends and is resolved to do it, based on the Prophet's (peace be upon him) saying: "When one of you is concerned about a matter," and "When one of you intends to do something." There is no scope for Istikhara without a matter that concerns you or about which you are resolved. However, if marriage to this man is proposed to you, or if you wish to propose yourself to him through your mahrams, then Istikhara is prescribed at that time. As for supplicating that this man becomes your husband, there is no harm in that.