Jones admits he almost left Stoke
The Trinidad and Tobago international has been linked with a move away from the Britannia Stadium on various occasions.
Asked if he had wanted to depart last season, Jones told Sky Sports News: "Yes, of course, because the atmosphere at the job wasn't good, and the entire squad can testify to that.
"Coming into work and the things we were doing, the way we were playing football - it was very discouraging for a lot of us and I think not only myself but a lot of players you would probably not have seen at the club come this season if the situation had remained the same.
"But we all know, things change sometimes pretty quickly in football and sometimes you just have to weather the storm."