The north London side are believed to be on the lookout for a number of attacking reinforcements as Arsene Wenger prepares to revamp his squad ahead of next season.
Arsenal are thought to have tabled a £20m bid to bring Vardy to The Emirates but the striker opted to stay at Leicester and has signed a new four-year deal with the Foxes.
That decision has forced Wenger to look elsewhere for attacking players and Portuguese outfit A Bola is now reporting that Arsenal are planning a bid to sign Slimani, who has a £24m release clause in his contract.
Tottenham have also been credited with an interest in the player, who scored an impressive 31 goals in 44 games for Sporting Lisbon last season.
Arsenal finished second in the Premier League last term.
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