The Gunners made the unusual bid to offset a clause in the Uruguay international's contract, which means the Anfield club must inform the forward of any offer for him above £40 million, according to the article.
Arsene Wenger has been linked strongly with Suarez this summer after the 26-year-old voiced his desire to leave Liverpool at a press conference while on international duty in May, as Andy Hunter of The Guardian reported at the time.
Suarez has linked up with the Liverpool squad in Australia after being allowed a later arrival following his appearances in the Confederations Cup with Uruguay.
According to a report from Mark Ogden of the Daily Telegraph, Arsenal's offer does not trigger a buyout clause, but it does mean the Merseyside club are obliged to inform the player of the bid.
But even with their strange offer, Arsenal are continuing an upward trajectory in bids for the striker after seeing a move of £30 million rejected earlier this month, as Tom Etherington of Goal.com reported.
Suarez had become a favourite among fans at Anfield since his £22.7 million move from Ajax in January 2011.
The striker has scored 51 times in 96 appearances during his Anfield career, but he is currently serving a 10-match suspension for biting Chelsea defender Branislav Ivanovic during a Premier League game in April.
But in spite of that, it doesn't look like Boston Red Sox owner Henry will be allowing Suarez to leave without a fight.