Liverpool's strike pairing have plundered 36 Premier League goals between them this season and both forwards were on target in Tuesday's 4-0 thrashing of city rivals Everton at Anfield.
Brendan Rodgers' men could have inflicted more Merseyside derby misery on neighbours Everton had Sturridge squared for Suarez to tap in with ease after 70 minutes instead of failing to spot the pass and chipping over himself - the England man also blazing a late penalty over the crossbar.
Suarez reacted theatrically to Sturridge's moment of selfishness, thrashing his arms wildly and aiming a few choice words at his team-mates.
While this type of incident is arguably replicated in most matches at all levels of the game, former Liverpool winger Barnes thinks it illustrates that Suarez and Sturridge may struggle to gel properly.
"They are not going to be a classic partnership because they are very individual," Barnes told talkSPORT.
"Yes, every now and again you will see there is a partnership in terms of movement and the passing to each other but, more often than not, all their work is going to be of their own making.
"That is what is going to be quite frustrating for either one of them, when they believe they are not getting the service or the passes from the other one.
"While they are two fantastic players, it is not a classic partnership.
"If anyone is going to look for a classic partnership between them, it is really not going to happen.
"That's not to say they are not both going to score lots of goals, but they will get frustrated and you will see some incidents like the one against Everton."
