The 25-year-old Pole is set to return to the Giallorossi at the end of this season, having established himself as one of the better keepers in Serie A.
And he has also recently broken into the Poland national team set-up, which makes him an interesting candidate for the Hammers.
However, reports in Italy claim Bundesliga outfit Hertha and Serie A side Torino are also keen on Skorupski.
Corriere dello sport claim Roma could be willing to do a deal with Torino if they include their attacking wing-back Bruno Peres in any agreement.
Skorupski moved from Poland's Gornik Zabrze to Rome in 2013 and his current contract runs until 2021.