The midfielder, despite the Dee's struggles in the Scottish Premiership has made a huge impact north of the border since his move from Arsenal last year.
Kamara, 22, is regarded as one of the best midfielders in Scottish football and his impressive displays have caught the eye of the Old Firm.
He underlined his progress this year with a strong performance in the draw at Celtic earlier this month.
Rangers are also keen and ran the rule over Kamara again in the 4-0 win at Ibrox recently.
But Swansea are looking to take the Finland international south, and he could be available for a cut-price £1million this summer.