The Gunners are understood to have identified the 24-year-old as their primary target ahead of the 2023-24 campaign, with Mikel Arteta's side allegedly confident of luring the midfielder to the Emirates Stadium.
Rice, who is widely regarded as one of the best midfielders in the Premier League, has developed into a star player for West Ham since making his senior debut in 2017, scoring 12 goals and providing 13 assists in 229 appearances across all competitions.
However, speculation over the England international's long-term future with the Hammers is rife, as he has less than 18 months remaining on his contract at the London Stadium.
Arsenal are expected to face competition for Rice's signature this summer, with the likes of Manchester City, Manchester United and Chelsea also said to be interested in his services.
According to The Guardian, via The Mail, Rice is 'almost certain' to leave West Ham this summer and the midfielder's most 'likely' destination is Arsenal.
The report adds that Rice is looking to play at a higher level as he has not been convinced that the Hammers are 'progressing'.
David Moyes's side were vying for Europa League silverware before securing a top-seven finish in the Premier League last season, but they have since suffered a decline in fortunes on the domestic front this term and are facing the prospect of relegation to the Championship, sitting just above the drop zone on goal difference.
Arsenal, who are understood to have been in contact with Rice's representatives over a potential summer transfer, were in the market for a new midfielder during the January window and eventually recruited Jorginho from Chelsea after failing to lure Moises Caicedo away from Brighton & Hove Albion.
Caicedo is still believed to be a target of Arteta's along with Rice ahead of next season, although the midfield duo could cost in excess of £100m, and a move for both players seems highly unlikely.
Towards the end of last year, Rice hinted that he would be open to seeking pastures new after expressing his desire to play in the Champions League - a competition Arsenal are on the cusp of qualifying for as the Premier League leaders sit 22 points clear of fifth-placed Newcastle United with 11 games remaining.
"One hundred per cent I want to play in the Champions League," Rice told reporters. "For the last two or three years I've been saying that. I've been playing consistently well for my club and I feel like I really want to keep pushing. I see my friends here who are playing Champions League and for big trophies.
"You only get one career and at the end you want to look back at what you've won and the biggest games you've played in. I really want to do that."
Meanwhile, West Ham sporting director and Rice's former teammate Mark Noble has reiterated the midfielder's ambition to compete in Europe's elite club competition, telling the Evening Standard: "It's just the world we live in. We're West Ham and these players want to go out and play Champions League football - and do you blame them?"
"Dec is no different. Dec will always be hailed at West Ham as a fantastic player and such a top, top person. But I don't think anyone begrudges him wanting to go and win things. We just hope he'll keep performing like he has been over the last month or so.
"Wherever Declan ends up, or however much someone pays for him, whether it's here or anywhere else, he's worth every penny. He's said openly he loves playing at West Ham, but he has got ambitions as a player to go and play in the Champions League and win trophies. I don't think any West Han fan can actually have an agenda over that."
To help fund a big-money swoop for Rice, Arsenal could reportedly look to sell Kieran Tierney, Nuno Tavares and Albert Sambi Lokonga during the summer transfer window.