Arsenal are reported to be ready to improve their inital £30million bid for Liverpool's wantaway Uruguay striker, and have also been linked with Real Madrid's £25m-rated forward Gonzalo Higuain and Everton midfielder Marouane Fellaini, as well as Manchester United forward Wayne Rooney.
So far, though, the free transfer of France Under-21 attacker Yaya Sanogo is Arsene Wenger's only confirmed summer purchase.
Graham - who captained Arsenal to the double in 1971 and then managed them on to the league championship twice in 1989 and 1991 as well as success in the League Cup, FA Cup and European Cup Winners' Cup - feels now is the perfect opportunity to raid the bumper Emirates Stadium cash reserves.
"Over the last few years Arsenal have not won a trophy and have spent a lot of money on the new stadium. Now is the time to spend money on top-quality players," Graham said on TalkSPORT.
"They need three or four quality players that can go straight into the first team. They have got quite a lot of money so it as an important summer for Arsenal and Arsene Wenger.
"They need an experienced second-choice goalkeeper, a top-quality physical centre-half, a holding midfield player and a finisher up front."
Liverpool are determined to keep hold of their star striker, who is still part-way through serving a 10-match ban for biting Chelsea's Branislav Ivanovic in a Premier League game last season.
Graham feels, despite the controversy surrounding Suarez, his ability as a player cannot be called into question.
"All the publicity that goes with Suarez takes away from how good a player he is. Suarez is one of the top strikers in Europe. If he comes to Arsenal, then he will get lots of goals," the Scot said.
Arsenal have arrived in Thailand for the next leg of their Asia tour following from a comfortable 7-0 win over an Indonesian side in Jakarta.
Midfielder Jack Wilshere missed Sunday's match with illness, but is expected to feature in the friendly at the My Dinh National Stadium on Wednesday.
Striker Olivier Giroud scored twice at the weekend and hopes it can help focus his mind on the battles ahead in the forthcoming campaign.
Speaking to Arsenal Player, Giroud said: "It is always good for a striker to score really early. It is a friendly game, but when you can 'kill' the keeper, you have to do it when you are a striker. You have to have the striker spirit.
"Now we will go ahead and improve."