The 18-year-old had the second-highest score and the fourth-best batting average of any player at this summer's World Twenty20 Global Qualifer.
"My big ambition is to really cement a place in the side in the second team for Sussex," he said.
"With a few good performances hopefully I'll be knocking on the door of that Sussex first team," he told BBC Jersey.
Jenner is about to start his second season with the Sussex Academy and made his debut for Jersey as a 15-year-old.
The wicketkeeper-batsman has become a regular in the island side, which currently play in Division Five of the World Cricket League.
Jenner has made a number of appearances for Sussex's second team and says playing international cricket for Jersey has prepared him well.
"It's similar to those international-type fixtures," he said.
"When we're playing in Jersey, sometimes we don't get the opposition that we might want, but this second team is a really good standard and it is similar to that international cricket.
"Sometimes it doesn't get taken too seriously, but I'm really proud to play for Jersey and I absolutely love coming back and playing for them.
"It's more high-level cricket, so it's all I can ask for really."
Jersey have yo-yoed between Division Four and Division Five of the 50-over World Cricket League, and host next year's Division Five tournament after being relegated from Division Four last summer.
But despite the inconsistency, Jenner thinks Jersey are capable of playing at a higher level.
"It's fairly disappointing," he said. "I think we're almost too good for World Cricket League Five and we haven't quite proved ourselves yet in Division Four."
Jersey's Jonty Jenner says he is hopeful that he can push towards the Sussex first team.