Unai Emery is desperate for fresh faces this summer as the Gunners look to bounce back from a disappointing campaign.
Arsenal finished fifth in the Premier League and missed out on Champions League football after being thrashed by Chelsea in the Europa League final.
Gunners chiefs will reportedly hand Emery £50m for transfers, with any additional signings to be funded by player sales.
And Arsenal have bid the majority of their initial budget on a double swoop on Sampdoria.
According to Tuttosport, the north London club have lodged a €42m (£37m) offer for Dennis Praet and Joachim Andersen.
Andersen is a centre-back and would go some way to fixing Arsenal’s leaky defence while Praet would provide creativity in midfield.
Sampdoria are willing to do deals for both players and AC Milan are also interested.
And Arsenal may have to up their bid in order to avoid missing out.
“Sampdoria are willing to do deals for both players and AC Milan are also interested.”
Tuttosport claim the Serie A giants would demand at least €50m (£44m) for the pair but may ask for even more.
Arsenal are likely to play hardball as they look for value in the transfer market.
Emery is in desperate need of defensive cover, as well as replacements for outgoing stars Petr Cech, Aaron Ramsey and Danny Welbeck.
Failure to qualify for the Champions League has made a huge dent in Arsenal’s budget.
Club chiefs were reportedly prepared to sanction £100m in signings had they beaten Chelsea in last week’s final in Baku.
Italian journalist Nicolo Schira has revealed who Arsenal’s first signing of the summer will be.
“The first purchase of Edu for Arsenal will be an amazing young talent: Gabriel Martinelli,” he wrote on Twitter.
“Gunners agreed to a deal which will see the Brazilian striker arrive in the summer from ItuanoFC after he will turn 18.”