With TNSE, there is rarely any indication of anything before it happens. So the lack of any indication that they tried to sign Perreault isn't evidence one way or the other that it happened or not. It's non-information.
And by the same token, if Perreault wanted to stay in Winnipeg, and there wasn't an offer already, he could have asked his camp to talk to Chevy.
To me, Perreault wanting to finish his career in his home province seems the most likely, given that the Jets seemed to really like him, are typically loyal to long-term players, and what he signed for was a bargain.