The combative 27-year-old, who is nearing full fitness following a knee injury, was the subject of a bid from the Latics a fortnight ago, with Roberto Martinez eager to be reunited with the player he took to the Liberty Stadium two years ago.
And Jenkins has revealed Wigan have returned with a revised offer which has also been rejected.
Jenkins told Swansea's official website: "The terms of the payment have improved, but our stance on Ferrie remains the same and the offer has been rejected.
"Ferrie is edging closer to full fitness and we are all looking forward to seeing him pulling on a Swansea shirt again and bolstering Paulo Sousa's squad."
Bodde was one of Martinez's first signings for Swansea, joining from ADO Den Haag for just £80,000. Martinez has already returned to Swansea to sign striker Jason Scotland and Jordi Gomez, who was on loan with the Welsh club last season.