The 19-year-old midfielder is expected to leave Bristol City after an excellent season in the Championship where he was deemed the Young Player of the Year.
There is serious Premier League interest in Scott and West Ham have already held talks with his representatives.
The Hammers are mulling over making a move for him but they could have to hurry as Serie A giants Inter are pushing to sign him.
According to Italian outlet Tutto Mercato, the Nerazzurri are serious about taking the young midfielder to Italy.
Inter have been keeping tabs on his performances and are now keen to secure a deal to sign him from Bristol City.
The Championship club are holding out for a fee in the region of €25m but Inter believe that they can knock down the price.
The Nerazzurri are pushing to sign him for somewhere around €18m from Bristol City this summer.
West Ham are interested in Scott but now could have to step up on their pursuit by tabling a bid.