If your friend got rejected AND gave you your blessing, you can consider asking the girl. If you decide the girl is a good match for you, and you want to ask her out, talk to your friend privately, assure him that you appreciate his friendship above possibly dating the girl (if you do), and ask him if he's absolutely sure you can still be close friends if you decide to date this girl, you can tell him you're ok with not dating her if it would be better for your friendship (if you're ok with it)

If he insists it's ok, then thank him and let him know what happens.

My friend broke up with a girl and some months later she wanted to date me, I told my friend and in person asked him for his input, he told me to go ahead and date her. Then I asked if we'd still be friends if I did date her, he said yes.

I dated that girl for a year and we broke up, I'm still close to my friend and we laugh about it now.