The 28-year-old is free to move clubs after seeing his contract with Lyon expire and the Welsh club are hopeful of a transfer, having also recently signed a new coach
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.
SWANSEA CITY LATEST
Swansea are 7/1 to beat Manchester United
"I think it's good to do things with caution," Jenkins told the Swansea Evening Post.
"He (Gomis) is still here and we are hoping to get things concluded soon."
The 28-year-old, who had scored 94 goals in 243 appearances for Lyon including 14 in the league last season, also helped 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."