The Three Lions host Peru this Friday before jetting off to Miami for warm-up games against Ecuador on June 7 and Honduras three days later.
Hodgson is likely to rotate heavily throughout all three games, but a report from The Mirror has claimed that the pair will be given ample opportunity to strike up a partnership ahead of the tournament in Brazil next month.
England begin their group campaign against Italy on June 14, and Hodgson wants to see how his forwards can co-exist in the friendly games against the three different South American opponents.
Sturridge plundered an impressive 21 goals last term, while Rooney hit 17 despite a wretched United campaign.
Hodgson told reporters: "We haven't really seen them [together], have we?
"We've seen an awful lot of the Sturridge-Suarez partnership at Liverpool but not a lot of Rooney-Sturridge partnership because they haven't had a lot of time to play together.
"Now's our chance. From the time we get to St George's Park we start to move away from bigger focus on fitness and getting people in the right shape to tactical preparation.
"That’s when the partnerships will start to develop. It won’t just be Rooney-Sturridge, we will be working on (Danny) Welbeck and (Rickie) Lambert as well."