Indeed, Southampton signed the striker from QPR for just £4 million earlier this month.
And Thompson told the Mirror: "Aside from [Christian] Benteke, we've not got an out-and-out striker. They were trying to fill that void with [Alex] Teixeira but that's not going to happen until the summer.
"They should have signed Charlie Austin. It's a case of needs must and for the price Southampton paid he would have been worth a gamble. And he's a Liverpool fan."
Austin's quality is clear for all to see and Liverpool aren't the only club that could have moved for the 26-year-old. Newcastle United still need a striker, while Tottenham, Sunderland and many more all need goals from a secondary (or in many cases primary) source.
As far as the Reds are concerned, it doesn't seem as though a new striker is coming any time soon. And, whenever a new forward is signed, it never seems to be the right one for Liverpool.
It's almost as if, in an attempt to find the next Luis Suarez, the Anfield club have overcomplicated things to such a degree they can no longer find a striker who can even do the basics on Merseyside.