Wallace was called into the Scotland squad by national boss Gordon Strachan last week as a result of his impressive displays for the Gers this season.
Nevertheless, Smith is still determined to push for a place in Ally McCoist's starting line-up in his preferred position in the weeks and months ahead.
And the born-again Ranger, now in his second stint with the Ibrox club where he started his football career, reckons that will have positive benefits for the team.
"Lee is obviously a great player and is currently involved in the international set-up," he said.
"But if I can push him then I can maybe get that wee bit more out of him and make his performances even better than they have been.
"My aim is obviously to be involved in competitive games here. But if I can create competition for places and improve the team's performances that will do me."
McCoist can pick Smith - and all of his other new signings - for competitive matches now after the year-long SFA signing embargo expired on August 31.
The 28-year-old was unable to be involved as a trialist in the opening games of the 2013/14 campaign because the last club he was registered at was not in Scotland.
The versatile player, who is equally comfortable playing in midfield as he is in defence, is looking forward to playing again after spending nearly a year on the sidelines.
Smith has not played in a competitive fixture since last turning out for MLS club Portland Timbers in the United States last October.
His time out of football has been difficult for the Scot and he is looking forward to being involved with Rangers in SPFL League One this season.
The defender is confident that, despite his lack of match action, he will be able to play an active part in the second stage of "The Journey" up the leagues.
He declared: "I have worked hard since coming back from America. The club gave me training facilities and I have used them to my benefit.
"I have done a lot of work over the summer as well so I am feeling good. There is still work to be done, but I am heading in the right direction."
"I knew how important getting a good pre-season under me belt would be for me and that is what I focused on doing."
Smith added: "When I left Portland Timbers, I didn't think it would take so long to get back playing again, but that is the way it has worked out.
"When the games I couldn't play in came along I just dealt with it.
"It was difficult, but now that I can play in competitive games I am looking forward to being involved."
Rangers is a very different club now from when Smith departed for Norwich City back in 2010.
The Bellshill boy broke into the Gers first team when Alex McLeish was manager in 2004 and many expensive foreign imports were still at the Glasgow club.
He started for the Light Blues in their Champions League last 16 match with Spanish club Villarreal and played with the likes of Thomas Buffel, Brahim Hemdani and Dado Prso.
But Smith is excited to be involved in McCoist's youthful side and is confident the likes of Fraser Aird, Robbie Crawford and Lewis Macleod will continue to be involved.
He saiD: " There are a lot more younger players involved now than there were in the past, but I think that is to the benefit of the football club in general. They are all doing well.
"It is sometimes hard when you see experienced players coming into the squad ahead of you.
"But all they have to do is work hard, keep doing what they are doing and they will get their chance. When they do, I am sure they will take them."
Nor is Smith, who has graced the biggest stadiums in England and Scotland, bothered about playing at grounds like Gayfield, Ochilview andf Somerset Park against part-time teams in the third tier.
"Playing at smaller venues doesn't bother me at all," he stated.
"It is part and parcel of where the club is at the moment and I am enjoying every minute of it. I am sure the rest of the players will be same.
"The players who came into the club knew what they were coming into.
"When you go to difficult away grounds you have to stick together and earn the right to play. Then you take it from there.
"I know what we are going to get. It is going to be a battle every week.
"We have to earn the right to play.
" That is the same wherever Rangers play whether it be in the top flight or in the bottom tier. But I am looking forward to it."