The Gunners are reported to have lodged two rejected bids for the controversial Uruguayan striker - one offer is said to be worth £40,000,001 - following his comments that he wants to leave Anfield.
"Arsene Wenger bangs on about having money to spend, but the reality is he doesn't like spending it," Lawrenson wrote in the Liverpool Daily Post. "But I'm convinced Suarez believes he is going to be an Arsenal player.
"The evidence all points to that. And if he thinks he might have to stay at Liverpool, I'm sure there will be a different modus operandi from Suarez and his agent."
Reports have claimed that Liverpool will not consider a bid less than £50m for Suarez.