The Gunners are desperate for fresh faces this summer as they look to bounce back from a disappointing campaign.
Unai Emery failed to secure Champions League football in his first season as Arsenal finished fifth and lost the Europa League final to Chelsea.
Gunners chiefs are reportedly willing to provide a £50m transfer budget, with any additional funds to be raised by player sales.
Reports earlier this week suggested Arsenal had been rebuffed with an initial €42m (£37m) bid for Sampdoria pair Dennis Praet and Joachim Andersen.
Emery wants Praet as a replacement in midfield for Juventus-bound Aaron Ramsey.
And Andersen would bolster his defensive options.
But while Arsenal are ready to up their offer, they face competition.
The transfer revelation comes amid news that:
“Emery is interested in Joachim Andersen, who is also a target for Milan and Tottenham.”
Italian journalist Nicolo Schira
Italian journalist Nicolo Schira tweeted: “#Arsenal insist for Dennis #Praet from #Sampdoria.
“Also #Emery is interested in Joaquim #Andersen, who is also a target for #Milan and #Tottenham.
“#Gunners are preparing a new bid, after that €42M (for both) rejected by Ferrero.”
Spurs are also expected to splash out this summer and maintain an interest in Andersen.
Toby Alderweireld has been linked with a move away and Mauricio Pochettino has identified Andersen as his replacement.
Meanwhile, Spurs are continuing to work on a deal for Real Betis star Giovani Lo Celso.
The playmaker is keen for a move and is seen as the ideal replacement for Christian Eriksen.
The Dane hinted yesterday that his future lies elsewhere amid reports of interest from Real Madrid.