The 26-year-old, who has scored nine Bundesliga goals this season, has previously been linked with moves to Arsenal and north east rivals Sunderland.
A fee of around £10 million has reportedly been agreed between the two clubs, with Cisse jetting in, having joined up with Senegal for the African Cup of Nations, to thrash out a deal.
If a deal is completed Cisse would join international teammate Demba Ba, a scorer of 15 Premier League goals this season, at the Sports Direct Arena.
With Steven Taylor out injured until the end of the season, manager Alan Pardew was expected to invest in defensive cover during the January transfer window.
However, following the collapse of the deal to sign Sochaux's Modibo Maiga, Pardew is seemingly keen to add to his attacking options instead.
Cisse struck 22 goals for Freiburg domestically last season, with only Bayern Munich's Mario Gomez netting more.
The club were criticised by supporters during the summer for not spending more of the £35 million recouped after the sale of Andy Carroll to Liverpool 12 months ago.
The only attacking addition, Ba, a free transfer from West Ham Untited, has proved to be a masterstroke for Pardew this term, helping the club to sixth in the Premier League.
With the cut price additions of Yohan Cabaye and Hatem Ben Arfa already paying dividends for Pardew, fans will be hoping the 50-year-old's knack of recruiting quality additions in the transfer market continues.