In the wake of their recent Capital One Cup success, the south Wales club are looking to increase the Liberty Stadium's capacity up to a maximum of 32,000 seats
The stadium, which opened in 2005 with a capacity of 20,750, has hosted regular sell-out crowds since the club's promotion to the Premier League in 2011.
And, though Jenkins is keen for work to start prior to the end of the season, he remains aware that the club's top-flight status is essential to any expansion plans.
"It all runs parallel to us still being in the Premier League and it being right for the club," he told reporters.
"We will have a full application in for the end of March and once that is passed, we will do part of that towards the end of next season, starting with the East Stand.
"If and when the final stage is complete, the stadium will hold 32,000. The first bit, which we plan to do this summer, will take the figure to 22,000 and then it will go up to 27,000 with the first stage of the East Stand, starting near the end of next season and running through the summer."
The club's recent victory in the Capital One Cup final ensured that the Liberty Stadium will host European football next season, and Jenkins is keen to establish training facilities worthy of that status.
Michael Laudrup's team currently train on a new artificial surface in Landore but this will soon be complemented by the addition of grass pitches and full dressing room facilities.
"The one in RTB (Landore) will be finished in the next few weeks," the chairman added.
"And planning permission has gone in for the one in Fairwood and has been approved for the first stage."