The forward bagged 17 goals for Gremio last season and he is now impressing for his country at the Olympics Games.
Both Leicester and Liverpool are interested, with the latter reportedly failing with an approach earlier in August.
And, according to RMC, the Premier League pair will now have to beat off competition from Rennes for Luan.
The French club are big fans of the 23-year-old and believe he could be tempted by a move to France.
Luan has constantly remained calm about his future and insists it will be sorted after Rio 2016.