The Gunners are said to be splashing £42million on midfielder Praet and defender Andersen.
The pair starred for Sampdoria as the club finished ninth in Serie A last season.
Praet could be a replacement for Mesut Ozil, who has been linked with a move away from the Emirates, while Andersen would tighten up a leaky Arsenal defence.
The Gunners conceded 51 Premier League goals last term, with Shkodran Mustafi coming under-fire for his performances.
Praet joined Sampdoria in 2016 and Andersen followed him through the door a year later.
La Gazzetta dello Sport claim Arsenal have ‘taken steps forward’ to finalise a deal for the duo.
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Arsenal’s 4-1 defeat to Chelsea in last month’s Europa League final and a fifth-placed Premier League finish saw them miss out on Champions League football for a third successive season.
But manager Unai Emery insists the club will still be able to attract top players in the summer transfer window.
He said: “I think Arsenal is a big name in the world of football. A lot of players want to play here.
“We are in one process and we need, in this process, to be strong in our idea, to be strong in our way.