The France international striker is a free agent after reaching the end of four-year stint at Lyon and has made no secret of his desire to move to the Premier League.
Gomis has been heavily linked with Swansea in the past month and the 28-year-old has reportedly spent time at the club this week discussing terms and undergoing medical checks.
Jenkins told the Swansea Evening Post: "I think it's good to do things with caution.
"He (Gomis) is still here and we are hoping to get things concluded soon."
Gomis scored 94 goals in 243 appearances for Lyon, helping them to the Coupe de France in 2012.
Swansea, meanwhile, have announced that Javier Garcia has joined as goalkeeping coach from Sevilla, where he was part of the backroom staff that helped to inspire the club's UEFA Europa League success last season.
The 34-year-old told Swansea's official website: "It was hard to leave Sevilla because it is such a good club with good people.
"But it's a great opportunity for me to work in such a positive environment where I can develop and grow with the club. It's an exciting challenge."