The duo forged a formidable partnership in the Premier League this season, scoring 52 goals between them in the English top flight as the Anfield club ended the season in second.
If Suarez is passed fit they are set to come up against each other when England face Uruguay in Group D on Thursday, and Sturridge says communication between the pair has been put on hold.
"I'm not on texting terms with Luis at moment," said England striker Sturridge, who scored his country's only goal in a 2-1 defeat to Italy on Saturday.
Suarez sat out his side's opening fixture - a 3-1 defeat to Costa Rica - due to a knee problem, but Sturridge is hopeful of lining up against him later this week.
"I hope Suarez is fit," he continued. "We want to play the best Uruguay team and we will go out and give it our best shot as a team.
"We need to negate Uruguay's threat. It's not just about Suarez or (Edinson) Cavani - it's a team game.
"We are looking forward to it, we're going out with a positive attitude and we are confident
"We go into games to win, when you don't get the result your performance deserves you are disappointed. I am hungry - it's a big occasion
"There is not much time between the games, and we can't dwell on last game. It's not a case of if we win, it's when we win
"We want to win to keep things in our hands. There is a lot of confidence, no nerves, no anxiety"
Sturridge also revealed he had been given some important words of advice prior to his goalscoring performance against Italy, adding: "I spoke to my mum on the day of the game.
"She told me to 'mash it up, son'. It was nice to see them on video phone."
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