Real Madrid, Chelsea and Manchester City have been among those touted as possible destinations for Laudrup, whose current deal at the Liberty Stadium runs to the summer of 2014, but Jenkins has no concerns he will lose the 48-year-old this summer.
Jenkins said: "Personally I have no issue about the thought of him not being here next season, I think he will be here and he's stated he would honour his contract. Michael has stated before he wants to be here next season."
He added: "If you look at his career before he came here, he needed to find the right club and stability in himself as a manager. He needed the time to show he could work in an environment for a period of years and be successful, which is what top managers are about.
"We felt before he joined this was the right place for that, which has proved to be the case. You would think in his own interests it is the right thing to stay with us and see where we get to next season."
On Tuesday, Swansea celebrated their Capital One Cup final success over Bradford with a bus parade through the streets of the city and a civic reception at the Guildhall.
Their 5-0 victory over the Bantams at Wembley gave the club their first piece of major silverware and they will experience European football for the first time since 1991, but has also increased speculation linking their Danish manager with some of Europe's top clubs.
Jenkins has previously stated his desire to tie Laudrup to a longer-term contract with the club and discussions have been progressing positively.
It is understood the pair have already discussed potential summer transfer targets as Swansea look to cope with the extra workload of Europa League football, although Jenkins acknowledges a new deal may not prevent Laudrup leaving at the end of next season.
He said: "We have been talking, but Michael touched upon it himself that if he had a 10-year contract it makes no difference (to the speculation). We have security until next summer when his current two-year deal finishes and we've got a period of time to make sure we have more security on that and that's something we will be looking at over the next few weeks."
- Sports & Recreation