The Swans enquired about Emnes at the end of last season and have been reported to have returned with a £3million offer for the Dutchman.
However, Jenkins told the club's official website, swanseacity.net: "We made an enquiry with Middlesbrough six weeks ago regarding Marvin's availability. We needed to test the water.
"But that was six weeks ago when Brendan Rodgers was the manager. We have certainly not made an enquiry since then.
"Having just appointed a new manager in Michael Laudrup, all current and new options are being assessed. Michael, with the help of the recruitment staff, will decide over the next few weeks the direction we take regarding potential new signings.
"It's important our supporters are aware of this and not to read too much into the host of names being linked with the club at present or in the future."
Emnes, 24, enjoyed a successful one-month loan spell at Swansea in October 2010. He became an instant hero after scoring the winning goal against south Wales rivals Cardiff.