The website claims that the Gunners, who had a bid in the region of £30 million turned down earlier this month, have offered £35 million up front for the unsettled Uruguayan, with a further £7 million in add-ons.
The Liverpool striker has made plain his desire to quit Anfield this summer in a series of interviews while away on international duty.
Suarez has cited his desire to get away from the English media, while also revealing he would like to play in the Champions League.
Liverpool boss Brendan Rodgers has repeatedly insisted that Suarez won't be sold this summer, although his stance softened slightly today when he conceded that an offer big enough would be enough to twist the club's arm.
"He's a player that obviously is talked about and there's been a been a lot of speculation over the course of the off-season," he said.
"But the reality is that he's a player that's very much valued at Liverpool.
"Unless there's any sort of offer that comes in which is anywhere near his value then there's nothing to consider and we haven't had that.
"So at the moment, in this present moment in time, he's back in, he's reported as he should do for training at the right time.
"He's had a good rest and he's now looking forward to getting fit with the rest of his team."
Should Arsenal be successful with their move for Suarez, he would become the club's record signing, surpassing the £15 million they paid for Andrei Arshavin in 2008.
The move represents a major change in Arsenal's approach to the transfer market as they look to flex their financial muscle.
Boss Arsene Wenger has so far been frustrated in his attempts to land Gonzalo Higuain from Real Madrid, who are said to be holding out for €37m, with Napoli believed to be leading the race for the Argentinian's signature.