Partey has been out since the end of October after injuring his thigh during a shooting drill in training.
The 30-year-old underwent surgery in early November to solve the issue and was left out of Ghana's squad for the Africa Cup of Nations this month.
But Partey is now nearing a return and it is understood that he has taken part in first-team training.
Given his injury record and the length of time he has been out for, Arsenal will not rush his comeback.
But Partey could make the squad for next Tuesday’s trip to Nottingham Forest in the Premier League.
Rice will be assessed by Arsenal medical staff this week but there is confidence that he will be available to face Forest.
The England international has been in fine form since his £105million move from West Ham in the summer and has missed just 73 minutes of Premier League football this season.
Arsenal have a clear week before they travel to Forest, having been knocked out of the FA Cup, and the squad will train as usual at their base in London Colney.
The players had some time off at the start of this week, but have since been training as normal ahead of the Forest game.