The English midfielder is one of the hottest properties in Europe and in the Premier League.
He has recently rejected signing a contract extension with the Hammers as he intends to push for a move this summer.
Manager Mikel Arteta is apparently directly in talks with the midfielder as Arsenal earmarked Rice as their top target.
Rice has been one of the few consistent players in the Premier League and West Ham could demand in excess of £100million for their club captain.
The 24-year-old has a better pass completion rate than Arsenal duo Granit Xhaka and Thomas Partey.
Alan Hutton believes Arsenal should sign Rice when the transfer window opens in the summer.
He tells Football Insider: “I think there is always a premium with English young talent and that is never really going to change.
“Do I think he is a £100m player? That is a lot of money. From what we have seen in recent windows that is about right.
“Arsenal, in the situation they are in at the moment in time, they are going for the league and pushing for trophies. That means they are going to have to strengthen every single window if they want to stay where they are.”
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