The 27-year-old Italy international is out of contract at the end of the season and is expected to leave the Stadio Artemio Franchi for pastures new.
AC Milan and Juventus are said to be interested in acquiring Montolivo's services but, according to talkSPORT, he favours a move to Old Trafford or the Emirates Stadium.
Montolivo is likely to have no shortage of offers when his deal expires, and the opportunity to move to the Premier League could prove too good to refuse for the Italian.
The former Atalanta playmaker has spent his entire career in Italy and, it is claimed, wants to challenge himself by joining a high-profile English side.
United or Arsenal would appear to fit the bill for Montolivo, and both are likely to consider midfield reinforcements when the transfer window reopens at the end of the season.