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.
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.