The 24-year-old joined Partizan in the summer of 2010 having been named the player of the season in the Veikkausliiga while playing for HJK Helsinki.
Kamara has since made 51 appearances for Partizan and has impressed with a number of composed displays both domestically and in Europe.
According to The Sun, his performances for Partizan have alerted both Chelsea and Liverpool while, it is claimed, he would favour a move to Stamford Bridge.
The recent appointment of former Chelsea boss Avram Grant as Partizan manager could help the Blues broker a deal, with the Israeli still on good terms with Roman Abramovich.
Liverpool, meanwhile, have been linked with numerous defensive midfielders following the season-ending injury to Lucas Leiva in December.
However, the return of Liverpool captain Steven Gerrard has seemingly made midfield reinforcements less of a priority for Kenny Dalglish, who is reportedly after another striker.