The England under-21 international has hopes the Spaniard is a success at the Emirates, and wants to step up this season and prove himself for both club and country
Rodwell had a frustrating time last season as he suffering with injuries and inconsistent form, but is confident he can shine this term if given the chance.
The England under-21 international has seen the likes of Phil Jones, Chris Smalling and Danny Welbeck called up for senior duty and hopes he will follow in their footsteps.
"We all want to play for the seniors, so it starts here," Rodwell told reporters.
"I still speak to them on a regular basis and we are pleased for them.
"They have all done well at Manchester United and their respective clubs, so we wish them the best of luck."
He continued: "I think this is the season for me.
"Last season was frustrating for me. I had a lot of injuries and couldn't really get a pattern of football going and I wasn't really fit.
"But hopefully that won't happen this season and I can stay fit and I can get back-to-back games."
Asked if he felt he was ready to replace Arteta in the heart of the midfield, he said: "Yeah, definitely. If I'm asked to.
"I'm ready now. I feel fit, I feel sharp and focused."
He added: "It's a good opportunity for [Arteta], so we'll all wish him the best.
"He will be a miss but we've got a lot of young players who can fill in."
Everton signed Real Madrid’s Royston Drenthe and Argentine striker Denis Stracqualursi on loan on deadline day, and although the latter is relatively unknown for many, Rodwell believes he will fit in well.
"I think he scored a hat-trick against Boca Juniors, so hopefully he can get us a few goals," he said.
"And obviously Drenthe from Madrid - hopefully he can do the business.
"He will know Johnny Heitinga so will probably have spoken to him about Everton.
"Hopefully they will both be good for us."