The 23-year-old is considered one of the most talented young defenders in Serie A and was tipped for a move to Stamford Bridge back in 2016.
According to Italian media outlet Leggo, Chelsea scouts have been watching Romagnoli closely again in recent weeks with a view to signing the centre-back in the summer for around €45 million.
Romagnoli made his senior debut for Roma in December 2012 against Atalanta.
He joined Sampdoria on loan in September 2014 but returned to Roma the following year, before being sold to Milan on a five-year deal for €25 million in August 2015.