The England international is a leading target for the Gunners ahead of the summer transfer window.
Competition for the 24-year-old’s signature will be fierce but there is an optimism at Arsenal that they will be able to land their leading target.
Rice has less than two years left on his contract in east London and has no plans to extend, meaning this summer represents the last chance to demand anything close to maximum value.
Hammers boss David Moyes has previously suggested the club would be looking for a fee approaching the British record amount Chelsea spent on Enzo Fernandez.
That stands at £120m and even after West Ham’s win over Manchester United on Sunday, Moyes sent a message to Rice’s suitors.
“He’s probably the best English midfield player around and that’s why he’s going to be extremely expensive if anyone comes calling,” said the Scot.
With that in mind, former Arsenal defender Martin Keown has cast doubt on whether Arsenal or Liverpool could even afford to move for Rice this summer.
“I think Declan Rice is going to be too expensive for Arsenal, quite frankly,” Keown told talkSPORT.
“I think he will be too expensive for Liverpool as well who have been in the Champions League now for a number of years.
“He’s a player Arsenal will like but not with those costs involved, I think it’s too much. Looking at Arsenal’s business, I don’t think it’s a route they will go down.
“I don’t think they’ve got the money, even though the Champions League will bring some more revenue. I don’t see him as a player Arsenal can afford to buy.”