The former Liverpool defender cites legends of the past who have come and gone at Anfield.
Suarez was the subject of a pursuit from Arsenal last summer, and the Uruguayan even spoke of his desire to play for Real Madrid - now there are fresh reports linking him with a move away from Merseyside.
Ever since his display for Uruguay against England on Thursday - where he scored twice in a 2-1 win just four weeks after an operation on his meniscus - there has been more and more speculation surrounding his future, with reports linking him with a move to Barcelona and Real Madrid.
In his Daily Mirror column, Lawrenson wrote: "I can't say that I'm surprised Real Madrid and Barcelona are circling Luis Suarez.
"Despite his insistence that he won't be angling for a move, there is an air of inevitability about their interest in him.
"If it happens, Liverpool will move on. Over the years they've lost Hunt and St John, Keegan and Toshack and Rush and Dalglish.
"They'll survive. What works in their favour is that they will probably get in the region of £70-£80 million to cushion the blow."
Suarez played a massive role as Liverpool narrowly missed out on the Premier League title last season, as the Uruguayan scored 31 goals for the Reds to claim the golden boot along Player of the Year accolades.
It goes without saying that Liverpool will try their best to keep hold of their striker, and will be confident of doing so after denying him a move last summer, combined with the new contract that he signed in December.
There are also reports this morning saying that those at Anfield are confident of keeping hold of Suarez as there has been no contact from any other club, nor has the player or his representatives expressed a desire to sell the forward - who is seen as integral if the Reds are to mount a serious challenge to both the Premier League and Champions League.