Majoro has not played since sustaining a hamstring injury in City's 1-1 draw with Kaizer Chiefs on November 29, while Putsche sat out the 1-0 loss to Free State Stars before the festive break.
However, the duo are back at training, with Putsche leading the race to recovery.
"'Major' has been out since our game against Kaizer Chiefs which was in November," City spokesman Julian Bailey tells KickOff.com. "It was a problem with his hamstring if I'm not mistaken. He's obviously taken the time off and just underwent a rehabilitation programme.
"He's still not in full training, he is in partial training. But we expect him to be ready by the time the matches resume.
"There was an issue with Roland Putsche as well, but he's been doing a bit more work than Majoro at the moment, so he's closer to a full recovery."
City Boyz coach Eric Tinkler has no other fitness concerns heading into his team's league meeting with the struggling Lions of the North at Cape Town Stadium on February 7.
The Telkom Knockout champions, who share the summit with Bidvest Wits and SuperSport United, have 25 points from 15 games - 12 points more than 15th-placed Highlands.