The club seems intent on getting a replacement for the injured Nigel de Jong, who damaged his achilles tendon against Torino last weekend.
Corriere dello Sport has earmarked the Belgian and Dutchmen as Milan’s first targets.
In Strootman, Milan would get a similar player to the one that just left the club, Mark van Bommel. While Nainggolan is a personal preference of manager Massimiliano Allegri.
However, the value of both players could be considered excessive by Milan, as PSV Eindhoven reportedly want €20m for Strootman and Cagliari proved tough to crack for Juventus during negotiations last year.
Follow Louis Gibberd-Thomas on Twitter: @mercutio156