The 27-year-old Italian international will be available on a Bosman free transfer, and is poised to move to the Premier League.
Gunners boss Arsene Wenger sent assistant Boro Primorac to take in Fiorentina's 2-2 draw with Genoa in Serie A last Sunday - a game in which Montolivo scored and impressed throughout for La Viola.
The Frenchman made enquiries about Montolivo last year, but a move to the Emirates Stadium failed to materialise. As the club look to make a number of key signings at the end of the season, Arsenal could renew their interest in one of their long-term targets.
Montolivo - who was appointed Fiorentina captain midway through the 2009-10 campaign - is best described as a "regista", or a deep-lying playmaker. Though he prefers to operate in the middle, he can in fact play anywhere across the midfield.
His versatility is a valuable attribute that could prove decisive in Wenger's decision to step up his bid to bring him to north London this summer.