It is thought that Rice will make a decision before the start of the Euro 2020 qualifying campaign which begins in March and Rice's West Ham teammate Michail Antonio gave a positive update, from an Irish point of view, on where the young star's loyalties lie.
The German, who has been sidelined through injury but was passed fit for Saturday's game, did not travel to the London Stadium, with Emery saying, 'the players here are better for the match today'. "We need consistency over 38 matches", he said.
Mundo Deportivo reports that Suarez is keen on a move in order to reunite with his former boss Unai Emery, whose relationship with the 25-year-old is said to be a significant factor in Arsenal's attempt to lure the Spaniard over to the Emirates. "It's an issue that the club must see what is the best for him, for the player, for the club, for everyone".More news: Islamic State in 'final moments' in Syria
"The big opportunity for us is that we can take in our hands the possibility to be closer to them". It's also the opposition team.
It is the first time Arsenal have been beaten away from home by the Hammers since 2006, when Marlon Harewood's 89th-minute strike claimed all three points for the hosts at Upton Park.
"And then sometimes we are doing but like today [Saturday] we need to do more to be more competitive and to impose our idea and our quality".More news: Chez Reavie pulls off record-setting eagle barrage in Hawaii — Sony Open
Emery has an agreement with Barcelona's Denis Suarez but the Catalan club are stalling over a loan deal as they want a commitment from Arsenal to buy the player in the summer, something the Londoners are refusing to do.
The defeat dented Arsenal's bid to break into the top four, with the Gunners still adrift of Chelsea - who face strugglers Newcastle at Stamford Bridge later Saturday - in the race for a Champions League place. Not one player is for sale.
"Sometimes he is helping us, at other moments not helping us because of his injury or because maybe the match is not for him".More news: Winter Weather Advisory in effect; expect heavy snow in Chicago-area counties