Viola missed out on the talented footballer as he left Estoril to join the Lions this summer, but they have since continued to monitor his performances.
And according to O Jogo, Fiorentina officials have been further convinced that Jefferson would be a welcoming addition to the squad at Artemio Franchi.
As a result, they will attempt to sign him at the earliest opportunity, although it remains to be seen whether Sporting will be prepared to listen to offers.
The 25-year-old has showed a great deal of promise since arriving at Estadio Jose Alvalade from Estoril and went on to start 7 Primeira Liga matches.
Jefferson Nascimento, who had featured for Sao Caetano, Guaratingueta, Palmeiras, Gremio Prudente, Fluminense and Nautico in Brazil, has done well to prove his worth in Portuguese top flight and a big club move could be on the cards.