Handanovic, 25, has carved a stellar reputation for himself in Serie A with Udinese and has also been targeted by Bayern Munich in the past.
The Gunners have already seen a bid for Fulham's Mark Schwarzer rejected this summer as they look to bring in a new number one and are now ready to try and lure the Slovenia international.
Portugal keeper Eduardo was also reportedly offered to Arsene Wenger, but he has now joined Genoa.
Udinese are understood to be reluctant to sell Handanovic, who is one of their prized assets, but - after excelling in Slovenia's 1-0 defeat to England at World Cup 2010 - they could be hard pushed to reject a big-money bid from a bigger club.
With question marks continuing to hover over Manuel Almunia, Handanovic could be the man to bring some stability to the club between the sticks.
Stay here for all the team news, updates from the grounds and reaction throughout the day in the Premier League. Get in touch on Twitter at @GoalUK.
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Championship
Crystal Palace v Doncaster
Peterborough v West Ham
League One
Brentford v Oldham
Chesterfield v Charlton
Leyton Orient v Huddersfield
MK Dons v Bury
Rochdale v Notts County
Stevenage v Carlisle
Walsall v Colchester
Yeovil v Scunthorpe
League Two
AFC Wimbledon v Bradford
Accrington v Oxford
Barnet v Swindon
Burton v Gillingham
Crawley v Aldershot
Dag & Red v Northampton
Macclesfield v Plymouth
Port Vale v Crewe
It’s been a relentless news week on the International front, so here at Goal.com we’re going to sooth your pain with what promises to be a bumper day of Premier League action. I’m Josh Clarke and I’ll be holding your hand as we start to crank things up this morning.
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