I don't think the coach makes the biggest difference tbh. Players want the club, the money or maybe the project. The coach maybe if they're a specialist, like you're a midfielder who wants to play under Guardiola (I think Wenger used to be the specialist for giving U21s top level game time). Hazard signed for Di Matteo, Coutinho and Sturridge signed for Rodgers, Lukaku and Mata signed for Villas Boas.
When has Wenger ever attracted players anyway? Sanchez picked Arsenal over Liverpool, I doubt he picked Wenger over Rodgers. Same for Suarez I'm guessing. Ozil it sounds like there wasn't a big bidding war among the elites and Madrid wanted him out so we'll never know if he actually picked us or just accepted a transfer out of a club that wanted to replace him.