Suarez, who is in Australia with Liverpool ahead of their friendly with Melbourne Victory on Wednesday, signed a new four-year contract with the Anfield club last year.
The deal is believed to contain a clause that states Suarez must be informed of any bid made for his services over £40 million.
The £40,000,001 bid is thought to be the second Liverpool have rejected from the north-London club.
Arsenal striker Lukas Podolski said he had no problem with the potential arrival of the prolific scorer, who netted 30 goals in 44 games for the Reds last season.
Podolski's team-mate Olivier Giroud has also gone on the record as saying he would relish the chance to play alongside Suarez, and the German feels the same way.
"I'm not scared about big names because it helps the team and will help me when we play together. Every summer is the same. Players come in and others leave," Podolski said.
"I am always happy to play with the best in the world.
"But it's not about what is good for me, it's about improving the whole team.
"You have competition at every big club, particularly one the size of Arsenal. When all the players are fit there is big competition here."
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