There were questions about Laudrup's future earlier in the summer as speculation suggested he was unhappy with Swansea's transfer plans and a number of other clubs were reportedly interested in luring him away from the Liberty Stadium.
Jenkins is delighted that Laudrup stayed committed to the club, but there continue to be rumours that his time in charge could come to an end at the end of the season.
The Swans chairman is optimistic that will not be the case, and has set his sights on another successful campaign to keep the club moving forward.
"I hope this won't be Michael's last season with us," Jenkins told the South Wales Evening Post. "The last thing we wanted after last season was a change in manager, and nothing is going to change on that front.
"I hope we have a fantastic season, that we do really well in the Premier League and the cups and that Michael feels there is still growth in our club and that he can stay here for a few years yet.
"That's clear in my mind and I hope it is the case."
Jenkins is confident that Swansea can push on from what they achieved last season after making a number of early signings and enjoying a settled end to the summer.
He explained: "You look at the 19 teams we are up against in the Premier League. You can go through nearly every one and for one reason or another, I think we have had a far smoother end to our summer and a smoother preparation than the majority of them.
"That says something about us as a club - that we can deal with what we dealt with, get our business done and move on very quickly to get prepared for the new season.
"It will be interesting to see how the other clubs cope with what they have been through, whether it's a change in manager or a player wanting to leave.
"A lot of top-half sides are seemingly going to try to make signings right up until the end of the window as well, which I find a very strange way to run a club, but that's what they seem to do.
"Taking all that into account, we are quite well prepared, and it will be interesting to see how we measure up in the first month."