Rice is expected to leave West Ham this summer, with only one year remaining on his contract.
The 24-year-old has been linked with a move away from the London Stadium on numerous occasions, with Chelsea, Manchester City, Manchester United, and Liverpool all showing interest in the England international.
The Gunners may face competition from Rice’s boyhood club, Chelsea, but are said to be growing confident in their ability to secure his signature in a deal worth around €80 million.
West Ham have always maintained that any interested party must pay at least £100 million to sign Rice, though their bargaining power will continue to diminish as they fight to remain in the Premier League.
Rice is fully committed to West Ham’s relegation fight this season, but he has stated repeatedly in recent months that he wants to play Champions League football and compete for trophies.
The West Ham midfielder at the age of 24 has 39 England caps and fits Arsenal’s recruitment model of looking for young players with leadership experience and potential.