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 Luis 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.