Google launched the Trusted Store program back in 2011, their way of vouching for online merchants.
But if those merchants are fully HTTPS, based on Google latests recommendations and algorithms – they are currently out of luck.
Michael who has a fully HTTPS enabled site tried to apply but was rejected because his site was fully HTTPS. He posted his concern in the Google AdWords Help community and said:
Google did indeed respond, where Mini from the AdWords team said they are working on it:
When will it come exactly? Well, that is unclear but I suspect very soon.
Forum discussion at Google AdWords Help.
Update: This is now resolved.