Mikel Arteta’s Premier League leaders have long been admirers of the 24-year-old and made their interest first known during the World Cup in Qatar.
The Gunners have made Rice a major target for the summer and believe he can help take the club to the next level. Any deal is expected to cost between £80-100million, smashing the club’s transfer record.
Chelsea have been previously linked, but their interest is understood to have cooled.
West Ham expect Rice to leave this summer with the player honest over his ambitions, last speaking out while on England duty in Doha.
He said: “I see my friends here who are playing in the Champions League and for big trophies… you only get one career and at the end of your career, you want to look back at what you have won and the biggest games you have played in. I am really ambitious.”
West Ham have Rice under contract until 2024, with the option of triggering a 12-month extension, but their negotiating position has been weakened by a dismal league showing
David Moyes's side are in the relegation zone on just 15 points after 19 games, just months on from the manager outlining the club’s target of pursuing Champions League qualification this season to match Rice's ambitions.