The defender has rejected the offer of a contract extension at Roma, and Portuguese newspaper A Bola and Italian paper Gazzetta Dello Sport report that Chelsea have tabled an offer. Roma want between €35m and €40m for the Moroccan international.
Along with Chelsea, offers have reportedly been received from Manchester City, rivals Manchester United and Spanish giants Barcelona.
The 27-year-old is one of the most sought after defenders in Europe, along with Porto's Eliaquim Mangala and Borussia Dortmund's Mats Hummels.
But the report claims Chelsea are leading the race to sign Benatia as the player has a preference to play under Stamford Bridge boss Jose Mourinho.
Chelsea's defensive situation
In the wake of David Luiz's departure to Paris Saint Germain, Chelsea have money to spend and the need for another defender. John Terry is approaching the stage where he will not be able to feature in every Chelsea game, and while Gary Cahill impressed last season, he'll need a new partner long-term.
Branislav Ivanovic could be shifted inside, but the Serbian international has been excellent at right-back and it would be strange to alter his position just to accommodate Cesar Azpilicueta.
Tomas Kalas, who handled Luis Suarez during Chelsea's 2-0 win over Liverpool late in the season at Anfield, will spend the next season on loan at Cologne.
As a result, Mourinho has been linked with several defenders, including Benatia and Mangala. Both are expensive, but with the Luiz transfer fee in the bank, Chelsea can afford to spend lavishly and still within UEFA's financial fair play guidelines.
Benatia made 33 Serie A appearances last season as Roma finished second in the league to Juventus. He chipped in with five goals, and is a real threat from set pieces - just like Terry, the man he could ultimately replace.
And here he is in action against the team he could join...