Atletico Madrid have also shown significant interest in signing Lovren.
Chelsea will face competition from Atletico Madrid to sign Lyon centre-half Dejan Lovren.
Viewed as a long-term replacement to captain John Terry at Stamford Bridge, Lovren looked set to join the west London club this summer.
However, according the Daily Express, Atletico are also keen to sign the defender, and could use money from the sale of Radamel Falcao to fund the bid.
While the reported fee of £8.5m will not deter Chelsea, Lyon may now look to spark a bidding war for the Croatian.
With Terry in and out of the team under interim boss Rafa Benitez, it makes sense for Blues owner Roman Abramovich to pursue Lovren this summer, to ensure his new manager has a replacement for their long term captain before the start of next season.
The defender has made 23 appearances for Lyon this season, and scored twice.