Scott was not included in Thomas Tuchel's current England camp due to injury, but his stock continues to rise, amid constant transfer rumours over a possible January exit.
Chelsea reportedly saw a summer offer rejected, and Rice's Arsenal are now among the clubs interested in a 2027 bid, despite Bournemouth potentially demanding £100 million for the 23-year-old.
Rice was asked about his view on possibly competing with Scott for club and country and he hinted at the former Bristol City man being ready to make the step up.
"To be honest, Alex Scott playing was incredible. The way he's been playing for Bournemouth the last two or three seasons has been remarkable.
"The way he's being spoken about is totally right because of the levels he's set for himself and I totally understand playing for England comes with competition.
"When Arsenal signed Bruno Guimaraes, when we signed Zubimendi, when we had Myles Lewis-Skelly, Merino, Odegaard, you're competing with six midfielders at your club every day, so there's nothing different.
"Throughout my career there's been competition. It's normal."