The Belgian ace, 24, has emerged as a top target for the Gunners as new boss Unai Emery looks to bolster his midfield.
According to Gianluca Di Marzio, Arsenal have held 'concrete' talks with the midfielder's agent.
But the Gunners are not the only side scrambling for his signature this summer, with Juventus also closing in.
It is understood that the North London club are viewing Praet as an alternative for Roma midfielder Lorenzo Pellegrini.
Praet's £22m release clause is not expected to trouble Emery, who has access to all of the club's resources this summer.
The midfielder has made 69 appearances for Sampdoria since joining from RSC Anderlecht in August 2016.
Inter Milan, Roma and Napoli have also indicated their interest after Praet's stellar season in Serie A.
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The 24-year-old fuelled speculation that he could leave the Italian side by posting a heartfelt message to his Instagram after the final game of the season.
Alongside a picture of himself, he wrote: "I want to thank all of the fans for the amazing support this year. "
Praet established himself as a talented midfielder during his time with Genk, where he scored 20 goals in 139 matches.
Despite showcasing his best form to date, Praet did not make Roberto Martinez's World Cup squad.
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