Thousands of Swansea fans braved the freezing weather to greet the team who showed off their first major piece of silverware from an open-top bus following Sunday's 5-0 rout of fourth tier Bradford City at Wembley.
It earned them a place in Europe and further enhanced the reputation of Danish coach Laudrup who has been linked with Real Madrid following an impressive debut campaign in the Premier League.
"I hope that Michael's here for a few years yet. He's cemented his roots here in Swansea," Jenkins told Sky Sports.
"His family are here. I just hope he's still with us and we're firmly focused on working together and having a good season next year as well.
"At this level, the type of club we are, there's no doubt teams involved in the Champions League can be a big pull and we've just got to put up with that, do our preparation, and keep our fingers crossed."
Laudrup has emerged as a contender to replace Jose Mourinho at Real, with an online fans' poll making him the overwhelming favourite to take the job should the Portuguese quit.
The Dane joined Swansea in June with fans questioning whether he could build on the success of former manager Brendan Rodgers who guided them into the Premier League and then to an 11th place finish before leaving to join Liverpool.
Laudrup, who has had managerial spells at Getafe, Mallorca and Spartak Moscow, has emphatically answered the doubters by winning the club's first major trophy in their centenary year and guiding them to ninth in the Premier League after 27 games.
"He's come into the Premier League from La Liga and done exceptionally well. He's still hungry, because he's building his way through the leagues," Jenkins added.