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 is His slave and Messenger.
Whoever wants to marry should ask the people who are connected with this matter to suggest to him a woman for marriage, and then he should ask trustworthy people who know this woman.
As regards what is mentioned in the question, it may lead to some undesirable consequences, because if he moves from looking at one woman to another, he subjects himself to being accused with regards to his religion.
If a person acts according to the above guidelines, and he is not able to get engaged to one woman and then moves to another and looks at her, then this is permissible.
For more benefit, please refer to Fataawa 84875 and 88135.
Allaah Knows best.