Italian publication Calciomercato claimed at the end of July that the Gunners were interested in signing the 24-year-old midfielder along with former teammate Lucas Torreira before his switch to Arsenal.
But Arsenal opted not to make a bid for the Belgian before the closure of the summer transfer window even though his release clause was £23.2million.
It now appears that Sampdoria are keen to offer Praet a contract extension and increase his buyout clause as interest continues to grow, with the likes of Juventus, Inter Milan, Roma and Napoli reportedly monitoring the midfielder.
Due to a knee injury, Praet has only featured once so far for Sampdoria this season, starting in their 1-0 win over Viterbese in the Coppa Italia back in August.
Last season, the Belgian featured regularly alongside Torreira in the heart of Sampdoria’s midfield, making 35 Serie A appearances.
With Aaron Ramsey almost certainly on his way out of Arsenal either in January or at the end of the season and Granit Xhaka still receiving a mix response from the Emirates faithful, a possible move for Praet would be a positive one knowing he has played many seasons alongside Torreira in midfield.