The 23-year-old has been linked with a move to London for most of the summer with the Gunners also believed to be tracking the starlet, but new Iron boss Avram Grant had previously failed to tempt the French outfit to sell their prized asset, dubbed the 'new Thierry Henry'.
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A bid of £11.2 million for Remy was rejected by the Ligue 1 side last week, but West Ham co-owner David Gold and David Sullivan flew to Nice on Monday to discuss an improved offer following Remy's revealing comments.
"I have always liked the Premier League and I have always dreamed of playing in England,” he told L'Equipe.
“When a club like West Ham is tempted, it is always exciting. But nothing is done, the clubs have to find an agreement and Nice asks for a lot of money.
Without setting any ultimatums, I would like to know my future quite soon."
Bordeaux, Lyon and Arsenal have all been tipped to make bids for the France international and Nice coach Eric Roy has resigned himself to losing his star striker, providing the club's valuation of the player is met.
"I absolutely rely on him, but we have resigned ourselves," Roy said. "We had a verbal agreement, which was that he would spend two seasons at Nice having four-years on his contract.
"So now if an offer comes and matches what the club expects, indeed he will leave."
Arsenal boss Arsene Wenger has already lured Ligue 1 goal-getter Marouane Chamakh to London from Bordeaux this summer, but has also been linked with a move for Remy to further bolster his forward line with reports claiming Eduardo could leave the club.
Remy has previously spoken of his admiration for the Emirates Stadium outfit and hopes of one day playing under Wenger.
"Arsenal are the club I want to join. I won't deny they are my priority. Arsenal are a young, ambitious side and I love to watch them play. It is the ideal place for me," he said.
By James Martini
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