The 26-year-old has been sidelined since January with a knee injury, but has recently returned to training and is nearing his comeback.
This weekend's FA Cup semi-final against title rivals Chelsea will come too soon for the full-back, but Pochettino is hopeful of having him back available when his side host the Gunners.
"Arsenal, maybe. For Saturday, no. He's okay, he's doing well, he's still not with the group but he's at a very good level," he told reporters.
Rose had made 18 Premier League starts this season before his injury.