The Reds stormed to their first league title in 30 years last season, amassing 99 points and losing only three games.
While their rivals around them have heavily invested in their squads, Liverpool have only added left-back Kostas Tsimikas so far.
Thiago is a reported target, but last week, the midfielder played down speculation that he will be leaving Bayern Munich in this transfer window.
Jurgen Klopp’s side kick off their Premier League campaign with a clash against newly-promoted Leeds United at Anfield
Former Reds striker Collymore believes that the Liverpool players may start to begin questioning if they can move forward without any major incomings, and highlights Griezmann as the sort of signing that could push them forward.
‘Kop fans must be very concerned that Liverpool have made no big-name signings this summer,’ Collymore told the Mirror.
‘Where are the players whose arrivals would make the dressing-room sit up and think: ‘We’d better push ourselves even more this season because the gaffer is getting serious’?
‘Even with reinforcements it would be very difficult for the Reds to match last season’s form; without them it would be almost impossible.
‘Don’t get me wrong, we know the title-winners have an excellent mentality, so of course they will be competitive once again. Under boss Jurgen Klopp, that’s practically a given.’
‘The question heading into the new season has to be whether Liverpool have enough players to turn what is clearly a very good team into a generational team like the Manchester United side of the nineties and noughties,’ Collymore added.
‘United boss Sir Alex Ferguson created a dynasty by constantly freshening things up with marquee signings. Liverpool haven’t yet done that.
‘Rio Ferdinand arrived at Old Trafford as the world’s most expensive defender. Then you had players like Jaap Stam, Ruud van Nistelrooy and Juan Veron.
‘That’s why I like the Antoine Griezmann rumour – if Liverpool were to get the French international striker then the dressing-room would be thinking the cavalry had finally arrived.
‘But if you don’t have that you start thinking: ‘Hang on, we might yet lose Gini Wijnaldum, we haven’t really brought anyone in, can we push on?’