Johnson has missed Houston's last five games since suffering a right hamstring injury during a Week 4 win over Pittsburgh, which required minor surgery two days later.
He worked out last Monday, but was held out of practice after experiencing soreness.
Kubiak said Johnson's latest workout "went very good" but didn't know if the star receiver would be able to practice with the team on Wednesday.
"We're going to take it a day at a time, but we're back on the track to Andre getting back on the field here very, very quickly," Kubiak said.
"Hopefully that's this week," the coach said, "but I don't know. We'll see. But he's very upbeat, went through a tough little few days there [last week], but now we've come out of this thing fine and he's back on track."
The Texans have won three games in a row, improving to 3-2 since Johnson went down, and are getting ready for Sunday's road game against Tampa Bay. They have a bye after that, and it's possible Johnson could be held out until a November 27 game at Jacksonville.
Johnson had 25 catches for 352 yards and two touchdowns in the first four games this season and has scored 52 touchdowns with 9,516 receiving yards since 2003.