Johnson, who turns 32 on Sept. 23, said earlier this week that he was optimistic to make the Cardinals' 53-man roster despite two fumbles in Saturday's preseason game against the Atlanta Falcons.
"I'm getting better and better," Johnson told ESPN on Monday. "Me running the ball never really has been the problem but I think I've shown my hands have gotten better, catching the ball better and those types of things. I think I've really done all that I can do."
During the preseason, Johnson rushed 13 times for 41 yards (3.2 yards per attempt).
The Cardinals re-signed Johnson to a second consecutive one-year deal just before the start of training camp in July. Each of his past two seasons were cut short by injury after not missing a game due to injury in his first seven seasons.
Johnson was placed on injured reserve last season after suffering a groin injury in Week 4 that required surgery. In 2015, Johnson suffered a fractured tibia in Week 12.
Johnson finished the 2016 season with 95 yards and one touchdown on 25 carries in a backup role. His first six NFL seasons with the Tennessee Titans were highlighted by a 2,006-yard season in 2009, when he led the league in rushing, broke the NFL's single-season record for yards from scrimmage (2,509) and was named NFL Offensive Player of the Year. He has 9,537 career rushing yards.