In 2012, Mitt Romney named Beth Myers to head his running mate search as early as mid-April:
https://www.bostonglobe.com/news/nation/2012/04/16/mitt-romney-taps-longtime-aide-beth-myers-lead-running-mate-search/TBsilHHmMnYDW2ppVqGpkL/story.htmlThis was four months before he announced Ryan as his running mate. By mid-May (three months before he picked Ryan) the campaign had contacted some of the people they were vetting, in order to get more information:
https://uselectionatlas.org/FORUM/index.php?topic=153778.0This year the conventions are in the second half of July, so the timeframe is compressed. Yet it seems very unlikely that either nomination will be decided before the first week of June. And in the Republican case, there’s a strong chance that it will go beyond that. So when are they actually going to start this process?
I would think that the Clinton campaign, at least, would start this earlier than June. Though actually contacting people who you’re vetting may come off as presumptuous if not every state has voted yet, and Sanders is still in the race. On the Republican side, it’s a bit different, since the vice presidency could be used as a bargaining chip in a contested convention.