The Gunners famously bid £40 million plus £1 for the Uruguayan when he was at Liverpool in 2013, believing it would trigger a release clause in his contract, although the deal was immediately blocked by Reds owner John W Henry.
Arsenal's strikeforce has struggled to score goals this season, with first-choice frontman Olivier Giroud currently 15 consecutive games without finding the net in the Premier League this season.
"Sometimes a charismatic figure in the team can affect the rest of the players. I like South American strikers - Carlos Tevez, Gonzalo Higuain – players that always give full commitment," Lauren told Goal.
"Suarez, too. He scores goals, he comes back to defend, he’s got ambition and hunger – the player has to be charismatic so that the players in the dressing room look up to him like he's an icon."
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The former Cameroon international continued: "We have to mix up technical quality with physical presence in some departments.
"I’ve watched many Arsenal games, I’ve been to the Emirates Stadium many times. We have to change the style of players in certain positions - centre-back, in the middle - we need more balance between physical and technical players.
"In the last few years we haven’t done that and it would be something that could improve the team. We need to buy a striker – I’m not saying that Giroud isn’t good enough – he’s done a good job, but sometimes you need a charismatic figure."
Gunners boss Arsene Wenger has made no secret of his desire to sign a world-class striker in recent seasons, and having previously seen bids for Suarez and Gonzalo Higuain fall through, the Frenchman is expected to be in the market for a goalscorer this summer.
Chief transfer fixer Richard Law is currently based in his office at Arsenal's London Colney training ground and has started speaking to other clubs and agents about potential deals.