According to Italian newspaper Il Tempo, both Manchester clubs are ready to tempt Roma with sizeable bids for star men.
It has been an excellent season for Roma, who began with a record-breaking 10 consecutive wins and recovered from a mid-season lull to finish comfortably in second place.
This summer, the Giallorossi intend to secure the future of coach Rudi Garcia and then go in search of reinforcements to take the club to the next level.
However, Roma's key men have been noticed by some of Europe's biggest clubs and they may face a battle just to keep their current assets.
Midfielder Miralem Pjanic was widely linked to Manchester United, but has signed a new deal in the capital.
United have been keeping an eye on Strootman for some time but a torn cruciate ligament suffered in March ruled him out for the rest of the season and the World Cup.
Probable new Man United boss Louis van Gaal has a high opinion of Strootman having worked with him as Holland boss and the signing may be linked to his arrival.
Meanwhile, La Stampa insists in its article titled 'Manchester menaces Rome' that Manchester City are ready to pay £30m for defender Mehdi Benatia.
The Moroccan international centre-back came to Italy in 2010 when he joined Udinese and Roma signed him last summer for around £10m plus two co-ownership deals.
Benatia has been magnificent for Roma this season and even managed to score five times while acting as a rock in the heart of the defence.
He has previously been strongly linked with Manchester United, so if City have emerged as his main suitors it would be an interesting shift.