The long-serving defender stepped in as first-team coach following Michael Laudrup's exit in February, but it is unknown whether the 35-year-old will keep his job for next season.
After the Swans secured their Premier League status with a 4-1 victory over Aston Villa last weekend, Jenkins has claimed that a decision will be made in the best interests of the Welsh outfit.
"Over the next couple of weeks we are going to talk things through with Garry and reflect on his time in charge," the South Wales Evening Post quotes Jenkins as saying.
"The decision we are going to make will be a huge decision, and obviously it will be made in the best interests of the club going forward."
Swansea are 12th in the league table on 39 points with two games left to play.