The Gunners were in a transfer tussle with Manchester City to lure the midfielder from West Ham, with Mikel Arteta eventually agreeing a pay a British record for the player - a figure that was broken by Chelsea for Moises Caicedo just weeks later.
Rice joins a growing contingent of Arsenal players within the England squad, with Ben White, Aaron Ramsdale and Saka all established in the senior side and Eddie Nketiah hoping to make his first appearance in upcoming games against Ukraine and Scotland.
Saka, speaking to talkSPORT while on international duty, said of conversations with Rice earlier in the summer: "He’d ask a few questions and I’d answer them.
"I’d just try to give him the reassurance that he’d be coming to the right club and that the future is exciting for us.
"If he joined us, he’d make us better and that yeah, we can definitely achieve things."
Rice scored his first goal for Arsenal in Sunday's 3-1 win over Manchester United, firing home side into the penalty area deep into injury time before Gabriel Jesus sealed the victory minutes later.
"It was an unbelievable moment for him and his family," Saka said of Rice's goal. "Even the stadium, he said it was crazy when he felt the atmosphere. He’s right though, it’s really special to play there.
"I’m just happy he’s happy and that he’s performing, and he’s got his first goal as well, I don’t think there’s a better moment for him to get his first goal. So yeah, I’m happy for him."