Arsenal are said to be targeting their Champions League last 16 first leg on either March 4 or 5, or their trip to Manchester United on March 9.
Martinelli is set to miss the games West Ham and Nottingham Forest and is a doubt for the Champions League last 16 first leg, as well as games against Manchester United and Chelsea.
Saka was initially ruled out until March but Arsenal sparked excitement among supporters when they posted pictures of him training in the gym in Dubai last week.
Havertz tore his hamstring when blocking a shot in training in Dubai and Arsenal have confirmed he will not return until next season.
Arsenal face West Ham in the Premier League on Saturday before a trip to Nottingham Forest next Wednesday, as the run-in begins in earnest.