The 19-year-old, who has contributed one goal and one assist in four Danish Superliga games after breaking into the first-team last month, could be set for a move to England this summer.
Danish publication BT (via The Sun) claim Brondby are expecting to experience financial difficulties due to the season being suspended by the Coronavirus pandemic.
The report goes on to say that Brondby may have to sell their prized assets in order to balance the books and Slimane is thought to be on the list.
Arsenal are reportedly keen on luring the midfielder to the Emirates having been impressed with his performances for the Danish outfit this season and could land him for as little as £4million.
“It was probably some younger players that the clubs were watching, either Slimane in our team or Haksabanovic.
“Both were very good today.”
Arsenal have been linked with several midfielders already ahead of the summer transfer window and Slimane looks to be the latest if reports prove accurate.