Most influential would mean the manager who most impacted upon football?
In modern times, that's Michels. No Michels, no Ajax, no Barca, no Holland, no 'total football'. So no Graham Taylor's Watford, no Sacchi's Milan, no, well, you get the picture.
That's why FIFA voted him 'Coach of the Century'.
There's a good case for a couple of English managers who were about in the 30s (the ones who took football to South America and developed the passing game in Europe) but I'll settle with Michels.