The Dane has enjoyed a successful debut season with the Swans, leading them to their first-ever major trophy thanks to Sunday's 5-0 win over Bradford the Capital One Cup final at Wembley.
And, despite Laudrup being touted for a summer switch to Real Madrid as a result of his success, Jenkins has expressed his belief that the 48-year-old will stay put.
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"But Michael has stated he would honour his contract and we are looking a year ahead already. Personally I have no issue about the thought of him not being here next season."
Laudrup's current contract is set to expire in the summer of 2014, but Jenkins is confident of securing a new deal for the former Getafe manager.
"We've got security in place now as his current two-year deal finishes next summer," he continued.
"We've got a period of time to make sure we have more security on that, but that's something over the next few weeks we'll have to speed up a bit and talk a bit further."
Laudrup's agent Bayram Tutumlu also believes there will be no problems in agreeing a new deal with the south Wales club in the coming weeks.
"We have a very good relationship with chairman Huw Jenkins and negotiations take place in a positive spirit," he said.
"The club has expressed a desire to extend and Michael is very happy at the club - it's not complicated.
"But, right now, we will enjoy the triumph and then we'll find the time in the coming weeks to finish things," he added.