Rumours were rife in the press that Swansea were meeting Sousa to discuss a 'general drop in standards' which led to question marks over the former Portugal star's future at the club.
But following an encouraging meeting, Jenkins was happy to confirm that both he and the manager are committed to driving the club forward next season.
"The meetings were very positive,'' declared the Swans chairman.
"We discussed our season in general and preparations for next season.
"There was a frank exchange of views from both parties over the course of a few hours, which was encouraging.
"As a club we were disappointed with all the speculation emanating from Sunday's final game. I think a few emotional comments were taken totally out of context.
"What people should realise is that these sorts of meetings between the board and the manager happen at the end of every season – wherever we finish in the league.
"The clear message that came out of the meetings was that everyone is committed to continuing the general improvement the club has been making year on year.
"There will be no sitting back and pats on the back, because there is a realisation that the Championship is a very competitive league. But we are prepared for the tough battle ahead to maintain our position at the top end of the table.
"We will be working hard together over the summer. We will be using the time wisely to strengthen the whole club.
"What you've got to remember is that last summer was very traumatic after all the departures at the club.
"You've got to take into account that Paulo (Sousa) came in late and never had the full summer to prepare. This time the summer is clear to prepare and get the squad down to the level he wants, around 24.
"It's very important we use our budget and finances wisely. It requires hard work and commitment to hold on to our players as much as we can. It also requires hard work to strengthen the squad and find replacements if necessary.
"I can't reiterate enough that both parties are fully committed to driving Swansea City forward.
"And I can guarantee every fan out there that we will be fitter, stronger and better equipped for the challenge next season. We will hit the ground running.''