According to Sky Sports the Italian giants have contacted Fulham about the midfielder who is out of contract at the end of the season.
Johansen joined Fulham in a £2m deal in August 2016 and played a lead role in last season’s campaign which resulted in promotion via a Play Off victory over Aston Villa.
Fulham spent heavily in the close season but have rarely been out of the relegation places with Claudio Ranieri expected to be busy during the January transfer window.
Johansen was one of Neil Lennon’s final signings for Celtic, joining in January 2014 from Stromsgodset in a deal believed to be worth £1.5m. Five months later the midfielder was joined at Celtic by Ronny Deila.
His eye catching style was a feature of Celtic’s 2014/15 season but his form tailed off badly the following season.
Brendan Rodgers appeared keen to keep the Norwegian internationalist but with no sign of a new contract being agreed he was sold to Fulham for £2m.