The Hammers were able to keep hold of the 24-year-old last summer despite the intense speculation surrounding his future, with Manchester United believed to have failed with a big-money offer.
However, Rice is widely expected to be on the move at the end of this season, with the midfielder recently expressing a desire to join a Champions League club.
The England international has entered the final 18 months of his contract at the London Stadium, although West Ham have the option to activate a further year, which would take him until June 2025.
Rice is thought to be determined to push for a move this summer, though, with the Hammers potentially reluctantly willing to agree to an exit for a fee in the region of £100m.
Manchester City, Man United and Liverpool are among the clubs to be linked with the midfielder, while Arsenal have also been credited with a firm interest.
According to Football Insider, the Gunners are currently in pole position, with the Premier League leaders 'in sustained contact' with Rice's representatives over a move.
The report claims that Mikel Arteta's side are willing to pay the midfielder in excess of £200,000 a week, with the club looking to secure an agreement before the end of the season.
Rice has again been a vital player for West Ham this season, featuring on 28 occasions in all competitions, contributing one goal and three assists in the process.
The midfielder has played 22 times in the Premier League this term, but a disappointing campaign to date has left David Moyes's side down in 18th position in the table.
West Ham sporting director Mark Noble recently admitted that Rice could depart in the near future.
"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?" Noble told the Evening Standard.
"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. Do you blame him for having really big ambitions? Of course you don't. If he didn't, he probably wouldn't be as good as he is."
Barcelona and Real Madrid have also previously been linked with Rice, but it is believed that he will remain in the Premier League this summer.