Standard Sport understands contact was made on Monday to discuss a potential fee for the 23-year-old, a day after Mitrovic left for Al-Hilal in a club-record sale worth £46million.
Kean was once considered one of Italy's finest young talents, but an ill-advised move to Everton stalled his development before returning to Juventus earlier this year.
The 23-year-old is mostly consigned to a substitute role at Juve, so far scoring 22 goals in 103 matches over two spells.
Arsenal striker Folarin Balogun is also being considered as Marco Silva demands a replacement for Mitrovic despite signing Wolves's Raul Jimenez earlier in the summer.
Fulham have also cooled their interest in Callum Hudson-Odoi after failing to agree a fee with Chelsea in summer-long talks.
Marco Silva wants a wide forward and Everton’s Demarai Gray is among those admired. The manager has told the club he wants two full-backs, a midfielder and a winger before the transfer window closes on September 1.