The Welsh club have brought in a host of signings ahead of Monk's first full season in charge, including the likes of Bafetimbi Gomis, Lukasz Fabianski, Gylfi Sigurdsson and Jefferson Montero.
However, Michu has left for Napoli on loan, while Ben Davies and Michel Vorm will ply their trade with Tottenham this season.
Ahead of their Premier League opener against Manchester United on August 16, Jenkins feels any remaining transfer activity will happen before they take on Louis van Gaal's men.
"Garry and his staff are looking to do one or two things to make sure we get the squad to where we want it to be over the next week or so," the Swansea chairman told the South Wales Evening Post.
"I wouldn't say there's a lot of work to be done.
"We are just looking to get one or two things done so we are where we want to be at the start of the season."
Defender Chico Flores is set to leave the club, having been heavily linked with Qatari outfit Lekhwiya - managed by former Swansea boss Michael Laudrup.
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