When Naruto is training with Jiraiya. It's the Leaf's plan to protect Naruto from the Akatsuki. Why didn't the whole team of Akatsuki attack them. I'm sure they can finished them off. Plus Black Zetsu is a sensory type, which means he can easily detect Naruto's whereabouts. So, why doesn't the Akatsuki as a whole attack Naruto directly while he is training with Jiraya?
Your question is a tad bit hard to understand, but I believe you're asking
"Why doesn't the Akatsuki as a whole attack Naruto directly while he is training with Jiraya?"
WARNING: SLIGHT SPOILERS BELOW. READ AT YOUR OWN RISK!
Before I explain my research, I will provide a tl;dr below:
TLDR: They did not have the manpower, people and structure to perform the task at the time.
The answer to this is because of how the Akatsuki operate. In the anime when the Akatsuki have their meetings after capturing Gaara, it is said that each member has a job of finding and retrieving a Tailed-Beast from the separate ninja clans. It is also shown that once a beast has been retrieved, a lot of chakra is required from all of them together to actually remove and contain the beast's power. When Deidara (Akatsuki guy with the clay bomb technique) captures Gaara and then targets Naruto, he is called out by other members as being called greedy for taking "more than one target". It is also shown that the Akatsuki hunt in pairs as they have always been shown. My answer to your question has many points. The first is that the Akatsuki are a conglomerate of rogue ninja, therefore they do not want to operate as a huge team as there is a great deal of tension amongst the characters. Second, the person who was supposed to get Naruto's beast was Itachi, but he was staving off due his confrontation with Sasuke.
Lastly, as stated here, it would have been IMPOSSIBLE to do this when he was younger because the 3rd and 4th Hokages could and would have killed them all, no question.
Even when Tobi attacked Naruto at birth, he failed to steal the beast because Minato was too OP for him. And even when he was in training with Jiraiya they weren't that powerful because Jiraiya had been tracking them, and speaks about them getting bigger learning new techniques but nobody knew their motives back then so they weren't a threat.
It was noted in Chapter 353, page 5 that using the Sealing Technique: Phantom Dragons Nine Consuming Seals that Akatsuki use to seal the bijuus in the Demonic Statue of the Outer Path, the bijuu needs to be sealed in order from Ichibi/One-Tail (Shukaku - Gaara) to Kyuubi/Nine-Tails (Kurama - Naruto) based on their number of tails.
Because of this, rather than unable to attack Naruto while he is training with Jiraiya or they did not have the manpower, people and structure to perform the task at the time. like Hikari claimed, it is more because they don't need to get Kyuubi at that time as they are still hunting the other bijuus.
Going with the time-line, Gaara was captured when Naruto finished his training. Which means that at that time the Akatsuki has not sealed even one bijuu since Gaara's Shukaku should go first to the statue. Thus, once again, no need for them to hunt the Kyuubi at that time.