The Gunners are desperate for fresh faces this summer as they look to bounce back from a disappointing campaign.
Unai Emery failed to achieve Champions League football in his first season in charge as Arsenal finished fifth before losing the Europa League final to Chelsea.
The Spaniard wants defensive reinforcements and is also hoping to add quality further up the pitch.
Praet and Andersen have been heavily linked in recent weeks and Arsenal have already seen bids turned down.
But according to Italian journalist Nicolo Schira, they’re confident of finalising the double deal after their latest offer.
He tweeted: “Tonight #Arsenal have sent a new offer to #Sampdoria for Joaquim #Andersen and Dennis #Praet: €48M for both.
“Steps forward for finalize the deal, even if Ferrero wants more.”
The transfer revelation comes amid news that:
“Arsenal have sent a new offer to Sampdoria for Joaquim Andersen and Dennis Praet.”
Italian journalist Nicolo Schira
Sampdoria are reportedly holding out for upwards of €50m (£44m).
But with the two clubs’ valuations so close, it’s increasingly likely that an agreement will be reached.
Andersen is seen as the key to plugging Arsenal’s leaky defence.
Laurent Koscielny has not been the same player since returning from injury while Shkodran Mustafi was heavily criticised this season and could leave.
Meanwhile, attacking midfielder Praet could be Aaron Ramsey’s heir.
The Welshman is joining Juventus on a free after failing to agree a new deal.
Arsenal reportedly have a transfer budget of £50m, with any additional funds expected to be raised through player sales.
And Emery is on the lookout for replacements for Danny Welbeck and Petr Cech, who have both been released.