The Gunners made a late move to bring the England international to the Emirates Stadium as Carroll pondered his £100,000-a-week offer from the Hammers.
The report claims Arsenal's enquiry was simply to find out exactly how much Liverpool wanted for Carroll, and they're understood to have backed out of talks when quoted figures around the £20m mark.
West Ham paid the Anfield club £16m up front, with another £3m in bonuses and performance-related clauses taking the actual figure up to £19m.
The striker penned a six-year £100,000-a-week deal with the option of a two-year extension after a successful loan spell with the Upton Park club last season. The total package could be worth up to £60m.
Carroll would not typically fit the mould of an Arsenal signing, but the report claims Arsene Wenger remains a fan of the player from his days at Newcastle.
The 24-year-old forward battered the Gunners on more than one occasion while with the north-east side, and Wenger has described him in the past as "special".
But his £35m move to Liverpool was a disaster, and the arrival of Brendan Rodgers signalled the end of his Liverpool career just 12 months after he signed.
Despite injury struggles, Carroll enjoyed a solid season last term and wants first-team football to consolidate his place in the England set-up before next year's World Cup.