Some associated with Liverpool have resigned themselves to Philippe Coutinho leaving, already assembling a list of targets to replace the Brazilian.
Barcelona were willing to part with around £114m, yet the Reds have remained firm in their stance he is not for sale.
However, if Liverpool do eventually offload Coutinho for what would be the second most expensive transfer in history, Reds legend Thompson has identified four players who he feels could improve Jurgen Klopp’s side with the money.
On a possible raid for Barcelona striker and former Liverpool star Suarez, Thompson said: “What they can do is try to find somebody out there, maybe even play Barcelona at their own game and say you can have Coutinho but we want Luis Suarez.
“Suarez might be unhappy with Neymar [joining Paris Saint-Germain]. You don’t know whether a player is unhappy or a club are willing to sell until you ask the question.”
The European Cup winning captain thinks Tottenham midfielder Alli would also add another attacking dimension to a Reds side without Coutinho.
“They could go after Dele Alli, who was a Liverpool supporter as a kid,” Thompson added. “Tottenham are a bit like Liverpool in that there’s always a price on a player.”
Aguero has plundered 170 goals in six years for Manchester City, and he would give Liverpool an attacking thrust up top, according to Thompson.
“Sergio Aguero is another player that might be interested if he’s not happy at Manchester City,” he added.
“But it comes back to being late in the window and that is the difficult situation Liverpool find themselves in.”
Perhaps the most realistic of the four is Arsenal midfielder Alex Oxlade-Chamberlain.
Thompson told Sky Sports: “Signing Alex Oxlade-Chamberlain would be a start and would be available for the right money with his contract situation at Arsenal, but the club need to be ready to move if they do sell so we’re not caught short.”
Liverpool are believed to have been monitoring Oxlade-Chamberlain’s contract situation at the Emirates this summer, but have yet to firm up their interest with an offer for the versatile England international.
Barcelona have previously bid £72m and £90m for Reds playmaker Coutinho, but Liverpool have no intention of doing business with the La Liga side.