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The Gunners completed a move for Schalke’s Sead Kolasinac last month and are understood to be on the verge of signing Lyon attacker Alexandre Lacazatte in the coming days.
A Bola claim that the north London outfit are now eyeing a £70million deal for winger Martins and defensive midfielder Carvalho ahead of the 2017/18 campaign.
Arsene Wenger is scouring the market for reinforcements this summer, with Arsenal desperate to improve on their disappointing season in the Premier League last term.
Liverpool are also expressing a strong interest in Portugal forward Martins so the Gunners may have a battle on their hands in the coming months.
The Merseyside club are reportedly lining up a £44m offer for Martins as Jurgen Klopp looks to bring more attacking options to Anfield after the signing of Mohamed Salah.
Manchester United have also been keeping tabs on Martins’ situation at Sporting in recent weeks.