The 28-year-old’s release clause is believed to have dropped to just £28 million this summer and Italian media outlet Calciomercato has claimed that the Premier League club will rival Inter Milan for his services.
Strootman played for Sparta Rotterdam, Utrecht and PSV Eindhoven before signing for Roma in 2013.
He has gone on to make 130 appearances for the Italian club in all competitions, scoring 13 goals.
Strootman made his senior international debut for the Netherlands against Austria in 2011.
He was a member of their squad at the European Championships the following year, but did not appear in any matches as the Dutch were knocked out at the group stage.