So what? He can pick someone even if he weren't running. Is there a law against choosing a running mate in an election?
...or he may not.
AP said he would pick in early June.
And yes it is legal to pick a veep before the nomination is official — just like it is legal for him to be president even though his dad was born in Mexico.
No, there’s no law against it, but it’s as unseemly as Callista Gingrich waxing melodic about what a wonderful First Lady she’d make.