The former Liverpool midfielder thought that the deadly strike duo didn't get on.
The duo managed to terrorise Premier League defences, and last season scored a combined total of 52 goals as the Reds finished as runners-up.
McAteer told the Daily Star: "I don't think they got on. Put it this way, I don't think they went out for dinner with one another.
"They worked well as a partnership but it was a love-hate relationship.
"Sometimes one would shoot instead of passing to the other, the next time it might be the other way round.
"They were probably trying to outdo each other and score more than the other - but it worked for Liverpool."
Suarez scored 31 goals with Sturridge finding the net on 21 occasions in the league last season for the Reds as the team was built around the free-scoring duo.
It's an interesting comment to make. A lot of the Liverpool side seems to get on with each of their teammates as Brendan Rodgers has assembled a closely-knit group at Anfield.
The suggestion that the two charged with delivering the goals for the Reds didn't get on may surprise a few people, but whatever their relationship was, it seemed to work when they were both in the side.
Given Suarez's departure to Barcelona in the summer, that's now one thing Liverpool won't have to worry about, if it was a concern at all.