The 22-year-old can play on the left and right side of defence, as well as in midfield, and he was first scouted by Antonio Conte's staff during the Blues manager's Juventus days.
Toljan was eligible to play for both Croatia and the United States but rejected those approaches to play for the country of his birth. He made his professional debut for Hoffenheim at 18 years of age in a 2-2 draw with Mainz.
His development has been stunted this season due to a limited number of first-team opportunities. However, Toljan is regarded as a major talent in Germany and he is expected to become a senior international in the future.
Napoli are seriously interested in the former Stuttgart player, who came to the attention of many of Europe's elite teams after an impressive showing at the 2016 Olympics. Germany won the silver medal in Rio and Toljan was one of the stars of the tournament, which alerted Bayern Munich and Juventus to his talent.
He boasts great physical attributes, while he is impressive going forward. Victor Moses and Marcos Alonso cover a lot of ground for Conte's side and Toljan is capable of matching Chelsea's current wing-backs in that regard.
His versatility is also a strength and he has been used in a variety of roles for Hoffenheim this season. He has provided his team with a goal and an assist, but there is a feeling that he has been increasingly sidelined at the club because he is letting his contract run down.
However, he has also lacked consistency this season and he has made the kind of defensive errors that wouldn't be tolerated under Conte.
He is, though, a low-risk rough diamond. He will need a lot of work - perhaps a loan move too - but Conte and many of his counterparts at top continental clubs see Toljan as a talent that is ready to be moulded into something special.
He will be available on the cheap with his contract expiring in June 2016 and Chelsea may look to immediately use him as a back-up option for Alonso and Moses.
However, the Blues may also look to loan him out to a club across Europe or even ultimately sign him to sell him on - as they did with the likes of Patrick Bamford and Papy Djilobodji, who were both offloaded on for a profit despite minimal first-team action at Stamford Bridge.
Chelsea will try to add more than just bargains in the summer and they will likely add another full-back even if they sign Toljan, with Roma's Antonio Rudiger, West Ham's Michail Antonio, Schalke's Sead Kolasinac and Monaco's Djibril Sidibe all under consideration.
Bayern Munich's David Alaba and Juventus' Alex Sandro have also been mooted as possible incomings for Chelsea's wing-back position, but they are not deals that are expected to be completed in the summer.